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Spatial regression models have recently received a lot of attention in a variety of fields to address the spatial autocorrelation effect. One important class of spatial models is the Conditional Autoregressive (CA). Theses models have been widely used to analyze spatial data in various areas, as geography, epidemiology, disease surveillance, civilian planning, mapping of poorness signals and others. In this article, we propose the Liu-type pretest, shrinkage and positive shrinkages estimators for the large-scale effect parameter vector of the CA regression model. The set of the proposed estimators are evaluated analytically via their asymptotic bias, quadratic bias, the asymptotic quadratic risks, and numerically via their relative mean squared errors. Our results demonstrate that the proposed estimators are more efficient than Liu-type estimator. To conclude this paper, we apply the proposed estimators to the Boston housing prices data, and applied a bootstrapping technique to evaluate the estimators based on their mean squared prediction error. [ABSTRACT FROM AUTHOR]

【Objective】There is a large population and strong demand for vegetables in Guangdong-Hong KongMacao Greater Bay Area (hereinafter called “the Greater Bay Area”). The evolution of vegetable production pattern and its influencing factors are studied in order to provide references for the spatial layout optimization and high-quality development of vegetable industry in the Greater Bay Area.【Method】The global autocorrelation indexes of vegetable gross outputs of each year were calculated to judge the regional correlation of vegetable production by using the statistical data at counties of the Greater Bay Area from 2010 to 2020 and the administrative map of the same year. The aggregation area of vegetable production and its spatial pattern evolution in counties were analyzed by local autocorrelation index. Spatial regression model was used to analyze the socio-economic factors affecting vegetable production under spatial correlation.【Result】From 2012 to 2020, the global autocorrelation index passes the test and the value is greater than 0, indicating that the vegetable production at county level forms a positive spatial correlation pattern, and the vegetable production has a certain degree of aggregation in space and increases with inter-annual changes. Through local spatial autocorrelation test and analysis, it is found that vegetable production areas such as Longmen county, Boluo county and Huicheng district shows a high-high aggregation pattern, and gradually forms an aggregation pattern in the northeast of the Greater Bay Area over time. The high-low and low-high spatial patterns of vegetable production are gradually affected by the positive correlation of adjacent areas, and finally forms the same pattern with the surrounding areas. Through the analysis of spatial regression model, it is found that the main factors affecting vegetable production are land, economic level, labor force and agricultural technology input in 2012. After 2016, the main influencing factor is land, while the influence of other factors is not obvious or significant, indicating that the expansion of vegetable planting scale is the first factor of yield increase.【Conclusion】There is a positive spatial correlation in vegetable production in Guangdong-Hong Kong-Macao Greater Bay Area, and gradually forms an industrial core area. In the future, it is necessary to increase investment in agricultural science and technology in the core areas of vegetable production such as Boluo, Longmen, Huicheng and Conghua, to further improve the modernization level of production, continuously drive the surrounding areas to improve the comprehensive industrial benefits, and promote the high-quality development of the vegetable industry. [ABSTRACT FROM AUTHOR]

Linear regression models are commonly used for estimating ground PM2.5 concentrations, but the global spatial autocorrelation and local spatial heterogeneity of PM2.5 distribution are either ignored or only partially considered in commonly used models for estimating PM2.5 concentrations. Therefore, taking both global spatial autocorrelation and local spatial heterogeneity into consideration, a global-local regression (GLR) model is proposed for estimating ground PM2.5 concentrations in the Yangtze River Delta (YRD) and in the Beijing, Tianjin, Hebei (BTH) regions of China based on the aerosol optical depth data, meteorological data, remote sensing data, and pollution source data. Considering the global spatial autocorrelation, the GLR model extracts global factors by the eigenvector spatial filtering (ESF) method, and combines the fraction of them that passes further filtering with the geographically weighted regression (GWR) method to address the local spatial heterogeneity. Comprehensive results show that the GLR model outperforms the ordinary GWR and ESF models, and the GLR model has the best performance at the monthly, seasonal, and annual levels. The average adjusted R2 of the monthly GLR model in the YRD region (the BTH region) is 0.620 (0.853), which is 8.0% and 7.4% (6.8% and 7.0%) higher than that of the monthly ESF and GWR models, respectively. The average cross-validation root mean square error of the monthly GLR model is 7.024 μg/m3 in the YRD region, and 9.499 μg/m3 in the BTH region, which is lower than that of the ESF and GWR models. The GLR model can effectively address the spatial autocorrelation and spatial heterogeneity, and overcome the shortcoming of the ordinary GWR model that overfocuses on local features and the disadvantage of the poor local performance of the ordinary ESF model. Overall, the GLR model with good spatial and temporal applicability is a promising method for estimating PM2.5 concentrations. [ABSTRACT FROM AUTHOR]

Many studies have identified the influences of PM2.5. However, very little research has addressed the spatiotemporal dependence and heterogeneity in the relationships between impact factors and PM2.5. This study firstly utilizes spatial statistics and time series analysis to investigate the spatial and temporal dependence of PM2.5 at the city level in China using a three-year (2015–2017) dataset. Then, a new local regression model, multiscale geographically weighted regression (MGWR), is introduced, based on which we measure the influence of PM2.5. A spatiotemporal lag is constructed and included in MGWR to account for spatiotemporal dependence and spatial heterogeneity simultaneously. Results of MGWR are comprehensively compared with those of ordinary least square (OLS) and geographically weighted regression (GWR). Experimental results show that PM2.5 is autocorrelated in both space and time. Compared with existing approaches, MGWR with a spatiotemporal lag (MGWRL) achieves a higher goodness-of-fit and a more significant effect on eliminating residual spatial autocorrelation. Parameter estimates from MGWR demonstrate significant spatial heterogeneity, which traditional global models fail to detect. Results also indicate the use of MGWR for generating local spatiotemporal dependence evaluations which are conditioned on various covariates rather than being simple descriptions of a pattern. This study offers a more accurate method to model geographic events. [ABSTRACT FROM AUTHOR]

In recent years, researchers' focus at semi-parametric regression models has increased, which is the effect of the integration between the parametric and non-parametric regression models. These models received a clear interest in most research and studies that take a more advanced and sophisticated nature in the process of accurate statistical analysis aimed at obtaining capabilities with a high level of efficiency. In this research, we deal with methods to address some problems, including the problem of autocorrelation between random errors, by relying on a semi-parametric partial regression model, which consists of two parts, a parametric part and semi-parametric one and merge the two parts in one of semi-parametric. This new regression contain strict constraints of the first and high flexibility of the later. Then we estimate the parameters of the parametric part using the general least squares method (SGLS) and the double residuals method (DR), also the Generalize Difference Based Liu Method)GDBL). As for the nonparametric regression model, we applied the core regression method using the Nadaray - Watson estimator and the Smoothing Spline method. The most important goal of this research is to create a semi-parametric regression model in which the methods used, both parametric and non-parametric, are applied, and make comparison to indicate the preference by relying on the Mean Squared Error (MSE) scale. [ABSTRACT FROM AUTHOR]

In this article, geovisualization is used for the presentation and interpretation of spatial analysis results concerning several house attributes. For that purpose, point data for houses in the region of Attica, Greece are analyzed. The data concern houses for sale and comprise structural characteristics, such as size, age and floor, as well as locational attributes. Geovisualization of house characteristics is performed employing spatial interpolation techniques, kriging techniques, in particular. Spatial autocorrelation in the data is examined through the calculation of the Moran's I coefficient, while spatial clusters of houses with similar characteristics are identified using the Getis-Ord Gi* local spatial autocorrelation coefficient. Finally, a model is developed in order to predict house prices according to several structural and locational characteristics. In that respect, a classic hedonic pricing model is constructed, which is consequently developed as a geographically weighted regression (GWR) model in a GIS environment. The results of this model indicate that two characteristics, i.e., size and age, account for most of the variability in house prices in the study region. Since GWR is a local model producing different regression parameters for each observation, it is possible to obtain the spatial distribution of the regression parameters, which indicate the significance of the house characteristics for price determination in different locations in the study area. [ABSTRACT FROM AUTHOR]

Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin–Watson pretest of the null hypothesis of zero first‐order autocorrelation of the random errors against the alternative hypothesis of positive first‐order autocorrelation. If this null hypothesis is accepted then the confidence interval centered on the ordinary least squares estimator is used; otherwise the confidence interval centered on the feasible generalized least squares estimator is used. For any given design matrix and parameter of interest, we compare the confidence interval resulting from this two‐stage procedure and the confidence interval that is always centered on the feasible generalized least squares estimator, as follows. First, we compare the coverage probability functions of these confidence intervals. Second, we compute the scaled expected length of the confidence interval resulting from the two‐stage procedure, where the scaling is with respect to the expected length of the confidence interval centered on the feasible generalized least squares estimator, with the same minimum coverage probability. These comparisons are used to choose the better confidence interval, prior to any examination of the observed response vector. [ABSTRACT FROM AUTHOR]

This study presents an alternative statistical methodology for estimating changes in land surface temperatures over mainland Southeast Asia (SEA). The method comprises of seasonal adjusting and autocorrelation filtering of MODIS LST time series obtained from 2000 to 2019 at systematic 45 sample locations. Furthermore, the filtered seasonal-adjusted LST time series were estimated to quantify the decadal change of LST using linear regression model. The long-term dynamic of temperature change was revealed by curve fitting using a spline model with different knots. The overall LST changes in sub-regional and regional scale were estimated using multivariate regression model which adjusted for spatial correlation and aggregated information of LST change from all individual sample locations irrespective of their strength of statistical evidence (p-value). The final result showed that the surface temperature change in the SEA region increases by 0.126 °C/decade. 95% confident interval for increasing ranges between 0.04 to 0.21 °C/decade, which shows evidence of substantial warming surface in this region. [ABSTRACT FROM AUTHOR]

This paper introduces the regression diagnostic methods for the Liu estimator under the general linear regression model with the autocorrelated error structure which is modeled by first-order autoregressive process. To identify the leverage observations, quasi-projection matrix is used, and to identify the influential observations DFFITS and Cook's D statistics which are single case deletion methods are used for the Liu estimator. For a special model with two explanatory variables, the leverage attitudes of the first observation are examined theoretically according to the autocorrelation coefficient and the Liu parameter. The proposed diagnostic methods are investigated through a numerical example. [ABSTRACT FROM AUTHOR]

In regression analysis, autocorrelation of the error terms violates the ordinary least squares assumption that the error terms are uncorrelated. The consequence is that the estimates of coefficients and their standard errors will be wrong if the autocorrelation is ignored. There are many tests for autocorrelation, we want to know which test is more powerful. We use Monte Carlo methods to compare the power of five most commonly used tests for autocorrelation, namely Durbin-Watson, Breusch-Godfrey, Box-Pierce, Ljung Box, and Runs tests in two different linear regression models. The results indicate the Durbin-Watson test performs better in the regression model without lagged dependent variable, although the advantage over the other tests reduce with increasing autocorrelation and sample sizes. For the model with lagged dependent variable, the Breusch-Godfrey test is generally superior to the other tests. [ABSTRACT FROM AUTHOR]

To explore the relationship between the geographical factors and P-R interval reference value of healthy adults, and to elucidate the geographical distribution of the P-R interval reference value in Chinese adults, to provide the basis for the standard of P-R interval reference value in different regions. The P-R interval reference value of 64,753 healthy adults in 341 cities (counties) level hospitals, research institutes, and universities in China was collected, and 15 geographical data and P-R interval reference value of healthy people were studied, and then 10 geographical factors with correlation were extracted for further analysis. Using spatial autocorrelation analysis to determine the autocorrelation of data space, using backward regression and ridge regression to construct forecast model, and the optimal prediction model is selected by comparing and evaluating the prediction effect of each model, the spatial distribution map of P-R interval reference value of Chinese healthy adults was constructed by statistical analysis. There was a significant correlation between normal reference value of adult P-R interval reference value and geographical factors. The regression model of normal reference value and geographical factors of adult P-R interval reference value was established by ridge regression analysis method: Y ̂ =149.2 + 0.02590X2 + 0.0005000X3 + 0.02634X5–0.05890X6 + 0.0008400X7 + 0.01606X8 + 0.2592X9–0.03638X12 + 5.888X13–0.2126X15 ± 8.6, and ArcGIS10.2. In the software interpolation method, the distribution chart of normal reference value of Chinese adult P-R interval reference value was inserted. Knowing the geographical factors of some places in China, we can use this model to estimate the P-R interval reference value in this region, and to obtain the normal P-R interval reference value between adults anywhere in China. [ABSTRACT FROM AUTHOR]

Residual spatial autocorrelation is a situation frequently encountered in regression analysis of spatial data. The statistical problems arising due to this phenomenon are well‐understood. Original developments in the field of statistical analysis of spatial data were meant to detect spatial pattern, in order to assess whether corrective measures were required. An early development was the use of residual autocorrelation as an exploratory tool to improve regression analysis of spatial data. In this note, we propose the use of spatial filtering and exploratory data analysis as a way to identify omitted but potentially relevant independent variables. We use an example of blood donation patterns in Toronto, Canada, to demonstrate the proposed approach. In particular, we show how an initial filter used to rectify autocorrelation problems can be progressively replaced by substantive variables. In the present case, the variables so retrieved reveal the impact of urban form, travel habits, and demographic and socio‐economic attributes on donation rates. The approach is particularly appealing for model formulations that do not easily accommodate positive spatial autocorrelation, but should be of interest as well for the case of continuous variables in linear regression. [ABSTRACT FROM AUTHOR]

The contribution of the conductivity to the spectrum of the generalized dielectric constant or susceptibility of molecular ionic liquids is analyzed, both in theoretical terms and computationally by means of molecular dynamics simulation of the concrete system 1-ethyl-3-methyl-imidazolium dicyanoamide at 300 K. As a central quantity the simulated current autocorrelation function is modeled by a carefully designed fit function. This not only gives a satisfactory numerical representation but yields the correct conductivity upon integration. In addition the fit function can be Fourier–Laplace transformed analytically. Both, the real and imaginary parts of the transform show expected behavior, in particular, the right limits for zero frequency. This altogether demonstrates that the components of the fit function are of physical relevance. [ABSTRACT FROM AUTHOR]

A figure of merit (FOM) has been developed for focusing quadrupole multiplet lenses for ion micro- and nanobeam systems. The method which is based on measurement of the central peak of the two-dimensional autocorrelation function of an image provides separate FOM for the horizontal and vertical directions. The approach has been tested by comparison with the edge widths obtained by nonlinear fitting the edge widths of a Ni grid and found to be reliable. The FOM has the important advantage for ion beam imaging of biomedical samples that the fluence needed is considerably lower than for edge fitting. [ABSTRACT FROM AUTHOR]

A quasiclassical method which enables evaluation of complex autocorrelation function from classical trajectory calculations is proposed. The method is applied for two highly excited nonlinearly coupled harmonic oscillators in regimes prevailed either by regular or chaotic classical motions. A good agreement of classical and quantum autocorrelation functions is found within short (Ehrnfest) time limit. Fourier transforms of the autocorrelation functions provide moderate resolved energy spectra, where classical and quantum results nearly coincide. The actual energy levels are obtained from approximate short-time autocorrelation functions with the help of filter diagonalization. This study is a follow up to our previous work [P. Zdanska and N. Moiseyev, J. Chem. Phys. 115, 10608 (2001)], where the complex autocorrelation has been obtained up to overall phase factors of recurrences. [ABSTRACT FROM AUTHOR]

We seek to use ARM MJO Investigation Experiment (AMIE)-DYNAMO field campaign observations to significantly constrain height-resolved estimates of the parameterization-relevant, causal sensitivity of convective heating Q to water vapor q. In field data, Q profiles are detected via Doppler radar wind divergence D while balloon soundings give q. Univariate regressions of D on q summarize the information from a 10-layer time–pressure series from Gan Island (0°, 90°E) as a 10 × 10 matrix. Despite the right shape and units, this is not the desired causal quantity because observations reflect confounding effects of additional q-correlated casual mechanisms. We seek to use this matrix to adjudicate among candidate estimates of the desired causal quantity: Kuang's matrix of the linear responses of a cyclic convection-permitting model (CCPM) at equilibrium. Transforming to more observation-comparable forms by accounting for observed autocorrelations, the comparisons are still poor, because (we hypothesize) larger-scale vertical velocity, forbidden by CCPM methodology, is another confounding cause that must be permitted to covary with q. By embedding and modified candidates in an idealized GCM, and treating its outputs as virtual field campaign data, we find that observations favor a factor of 2 (rather than 0 or 1) to small-domain 's free-tropospheric causal q sensitivity of about 25% rain-rate increment over 3 subsequent hours per +1 g kg−1q impulse in a 100-hPa layer. Doubling this sensitivity lies partway toward Kuang's for a long domain that organizes convection into squall lines, a weak but sign-consistent hint of a detectable parameterization-relevant (causal) role for convective organization in nature. Caveats and implications for field campaign proposers are discussed. [ABSTRACT FROM AUTHOR]

Abstract This paper is devoted to a method for the forecasting of seasonal time series. The core of our approach is based on the fuzzy transform and fuzzy natural logic (FNL) techniques. Under the assumption that a time series can be additively decomposed into a trend-cycle, a seasonal component and an irregular fluctuation, the forecasting is a combination of individual forecasting of each of these constituents. More precisely, the trend-cycle and the seasonal component are predicted with the help of fuzzy transform, pattern recognition and fuzzy natural logic techniques. To model the irregular component, we apply the Box–Jenkins approach. In the paper, we compare the suggested method with two other well-known methods, namely STL (see [14]) and ARIMA ones. [ABSTRACT FROM AUTHOR]

In this simulation study, regressions specified with autocorrelation effects are compared against those with relationship heterogeneity effects, and in doing so, provides guidance on their use. Regressions investigated are: (1) multiple linear regression, (2) a simultaneous autoregressive error model, and (3) geographically weighted regression. The first is nonspatial and acts as a control, the second accounts for stationary spatial autocorrelation via the error term, while the third captures spatial heterogeneity through the modeling of nonstationary relationships between the response and predictor variables. The geostatistical‐based simulation experiment generates data and coefficients with known multivariate spatial properties, all within an area‐unit spatial setting. Spatial autocorrelation and spatial heterogeneity effects are varied and accounted for. On fitting the regressions, that each have different assumptions and objectives, to very different geographical processes, valuable insights to their likely performance are uncovered. Results objectively confirm an inherent interrelationship between autocorrelation and heterogeneity, that results in an identification problem when choosing one regression over another. Given this, recommendations on the use and implementation of these spatial regressions are suggested, where knowledge of the properties of real study data and the analytical questions being posed are paramount. [ABSTRACT FROM AUTHOR]

The study of pollution in geographical areas includes spatial dependence, non-normal distribution, and heteroscedasticity. However, the modelling of edaphological data has not taken these features into consideration. Therefore, this study included the analysis and comparison of the behavior of the estimators of generalized linear regression (GLM), generalized linear mixed (GLMM), generalized additive (GAM), and generalized additive mixed (GAMM) models, through the simulation of a response variable generated with different statistical distributions, with five weighing matrixes (W, B, C, U, and S) and several autocorrelation levels. The results showed a strong U-adjacency matrix for all spatial autocorrelation levels. As was expected, GAMs and GAMMs were higher than GLMs and GLMMs, as a consequence of their flexibility which is represented by smoothing splines and the incorporation of mixed effects. The concentration of heavy metals and the risk probability of surpassing permissible limits in the Mezquital Valley, Hidalgo, were subject to prediction mapping. [ABSTRACT FROM AUTHOR]

Most theoretical studies have explored the evolution of plasticity when the environment, and therefore the optimal trait value, varies in time or space. When the environment varies in time and space, we show that genetic adaptation to Markovian temporal fluctuations depends on the between‐generation autocorrelation in the environment in exactly the same way that genetic adaptation to spatial fluctuations depends on the probability of philopatry. This is because both measure the correlation in parent‐offspring environments and therefore the effectiveness of a genetic response to selection. If the capacity to genetically respond to selection is stronger in one dimension (e.g., space), then plasticity mainly evolves in response to fluctuations in the other dimension (e.g., time). If the relationships between the environments of development and selection are the same in time and space, the evolved plastic response to temporal fluctuations is useful in a spatial context and genetic differentiation in space is reduced. However, if the relationships between the environments of development and selection are different, the optimal level of plasticity is different in the two dimensions. In this case, the plastic response that evolves to cope with temporal fluctuations may actually be maladaptive in space, resulting in the evolution of hyperplasticity or negative plasticity. These effects can be mitigated by spatial genetic differentiation that acts in opposition to plasticity resulting in counter‐gradient variation. These results highlight the difficulty of making space‐for‐time substitutions in empirical work but identify the key parameters that need to be measured in order to test whether space‐for‐time substitutions are likely to be valid. [ABSTRACT FROM AUTHOR]

The consistency of model selection criterion BIC has been well and widely studied for many nonlinear regression models. However, few of them had considered models with lag variables as regressors and auto-correlated errors in time series settings, which is common in both linear and nonlinear time series modeling. This paper studies a dynamic semi-varying coefficient model with ARMA errors, using an approach based on spectrum analysis of time series. The consistency property of the proposed model selection criteria is established and an implementation procedure of model selection is proposed for practitioners. Simulation studies have also been conducted to numerically show the consistency property. [ABSTRACT FROM AUTHOR]

Trade winds localized within the Western Equatorial Pacific express lagged and statistically significant correlations to sunspot numbers as well as to streamflow in rivers of the Southern Rocky Mountains. Both correlation sets were integrated in a linear regression analysis to produce relatively accurate sub-decadal streamflow forecasts for an annual and a 5-year average. In comparison to the autocorrelation technique, the prototyped method yielded the highest correlations, the highest goodness-of-fit scores, and the lowest root mean squared errors, for both the 5-year average and the annual average assignments. Of all of the cases examined, the highest Kolmogorov-Smirnov test scores between observation and prediction were found for the single solar-based forecast 5 years in advance for the 60-month average streamflow of the Animas River in New Mexico. [ABSTRACT FROM AUTHOR]

A method is proposed for accounting for serial correlation (autocorrelation) of data in the linear regression problem which enables accounting the autocorrelation on large scales. The residual series is represented as an autoregressive process of the order, k, that can be much greater than 1, and the autocorrelation function of the process is calculated by solving the system of the Yule-Walker equations. Given the autocorrelation function, the autocorrelation matrix is constructed that is included in formulas for estimates of regression coefficients and their standard errors. The efficiency of the method is demonstrated by the multiple regression analysis of data of 26-year measurements of the column NO2 content at the Zvenigorod Research Station of the Institute of Atmospheric Physics. Estimates of regression coefficients and their errors depend on the order of autoregression, k. First, the error increases with increasing k. Then it reaches a maximum and next begins to decrease. In the case of NO2, the maximum error is more than doubled compared to its initial value. The error decrease (after reaching the maximum) stops if k approaches the value at which the autoregressive process enables describing important features of the autocorrelation function of the residual series. Estimates of seasonally dependent NO2 trends and effects on NO2 of natural factors such as the 11-year solar cycle, the quasi-biennial oscillation, the North Atlantic Oscillation and others are obtained. [ABSTRACT FROM AUTHOR]

Ordinary least squares method is usually used for parameter estimation in multiple linear regression models when all regression assumptions are satisfied. One of the problems in multiple linear regression analysis is the presence of serially correlated disturbances. Serial correlation can be formed by autoregressive or moving average models. There are many studies in the literature including parameter estimation in regression models especially with autoregressive disturbances. The motivation of this study is that whether serially correlated disturbances are defined by a different type of nonlinear process and how this process is analyzed in multiple linear regression. For this purpose, a nonlinear time series process known as self-exciting threshold autoregressive model is used to generate disturbances in multiple linear regression models. Two-stage least squares method used in the presence of autoregressive disturbances is adapted for dealing with this new situation and comprehensive experiments are performed in order to compare efficiencies of the proposed method with the others. According to numerical results, the proposed method can outperform under the type of self-exciting threshold autoregressive autocorrelation problem when compared to ordinary least squares and two-stage least squares. [ABSTRACT FROM AUTHOR]

Series models have several functions: comprehending the functional dependence of variable of interest on covariates, forecasting the dependent variable for future values of covariates and estimating variance disintegration, co-integration and steady-state relations. Although the regression function in a time series model has been extensively modeled both parametrically and nonparametrically, modeling of the error autocorrelation is mainly restricted to the parametric setup. A proper modeling of autocorrelation not only helps to reduce the bias in regression function estimate, but also enriches forecasting via a better forecast of the error term. In this article, we present a nonparametric modeling of autocorrelation function under a Bayesian framework. Moving into the frequency domain from the time domain, we introduce a Gaussian process prior to the log of the spectral density, which is then updated by using a Whittle approximation for the likelihood function (Whittle likelihood). The posterior computation is simplified due to the fact that Whittle likelihood is approximated by the likelihood of a normal mixture distribution with log-spectral density as a location shift parameter, where the mixture is of only five components with known means, variances, and mixture probabilities. The problem then becomes conjugate conditional on the mixture components, and a Gibbs sampler is used to initiate the unknown mixture components as latent variables. We present a simulation study for performance comparison, and apply our method to the two real data examples. [ABSTRACT FROM AUTHOR]

The purpose of this research are: (1) to obtain spline function estimation in non parametric regression for longitudinal data with and without considering the autocorrelation between data of observation within subject, (2) to develop the algorithm that generates simulation data with certain autocorrelation level based on size of sample (N) and error variance (EV), and (3) to establish shape of spline estimator in non parametric regression for longitudinal data to simulation with various level of autocorrelation, as well as compare DM and TM approaches in predicting spline estimator in the data simulation with different of autocorrelation observational data on within subject. The results of the application are as follows: (a) implementation of smoothing spline with penalized weighted least square (PWLS) approach with or without consideration of autocorrelation in general (in all sizes and all error variances levels) provides significantly different spline estimator when the autocorrelation level >0.8; (b) based on size comparison, spline estimator in non parametric regression smoothing spline with PLS approach with (DM), or without (DM) consideration of autocorrelation showed significantly different result in level of autocorrelation > 0.8 (in overall size, moderate and large sample size), and > 0.7 (in small sample size); (c) based on level of variance, spline estimator in non parametric regression smoothing spline with PLS approach with (DM), or without (DM) consideration of autocorrelation showed significantly different result in level of autocorrelation > 0.8 (in overall level of variance, moderate and large variance), and > 0.7 (in small variance). [ABSTRACT FROM AUTHOR]

Spatiotemporal nonstationarity and autocorrelation are two crucial points in modeling geographical data. Previous studies have demonstrated that geographically and temporally weighted autoregressive (GTWAR) model accounts for both spatiotemporal nonstationarity and autocorrelation simultaneously to estimate house prices. Therefore, this paper proposes a kernel-based GTWAR (KBGTWAR) model by incorporating the basic principle of support vector machine regression into spatially and temporally varying coefficients model. The efficacy of KBGTWAR model is demonstrated through a case study on housing prices in the city of Shenzhen, China, from year 2004 to 2008. Comparing the existing models, KBGTWAR model obtains the lowest value for the residual sum of squares (RSS) and the highest value for the coefficient of determination R2. Moreover, KBGTWAR model improves the goodness of fit of the existing GTWAR model from 12.0 to 4.5 in terms of RSS, from 0.914 to 0.968 in terms of R2 and from 3.84 to 4.45 in terms of F-statistic. The results show that KBGTWAR model provides a comparatively high goodness of fit and sufficient explanatory power for both spatiotemporal nonstationarity and autocorrelation. The results of this study demonstrate that the proposed KBGTWAR model can be used to effectively formulate polices for real estate management. [ABSTRACT FROM AUTHOR]

In climate variability studies, lagged linear regression is frequently used to infer causality. While lagged linear regression analysis can often provide valuable information about causal relationships, lagged regression is also susceptible to overreporting significant relationships when one or more of the variables has substantial memory (autocorrelation). Granger causality analysis takes into account the memory of the data and is therefore not susceptible to this issue. A simple Monte Carlo example highlights the advantages of Granger causality, compared to traditional lagged linear regression analysis in situations with one or more highly autocorrelated variables. Differences between the two approaches are further explored in two illustrative examples applicable to large-scale climate variability studies. Given that Granger causality is straightforward to calculate, Granger causality analysis may be preferable to traditional lagged regression analysis when one or more datasets has large memory. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student’s) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model. [ABSTRACT FROM AUTHOR]

Power output from photovoltaic (PV) systems in outdoor conditions is substantially influenced by climatic parameters such as solar irradiance and temperature. PV manufacturers always provide technical specifications in laboratory conditions but reliable relationship for the power output must be determined for accurate prediction under real operating conditions. For the present study, solar irradiance G, temperature T and electrical power output P data under real conditions are methodically and regularly inscribed in dataloggers. Hence, in this paper, we investigate rigorous and robust statistical methods for small sample such as Augmented Dickey- Fuller and Engle Granger for stationary series to determine the estimate regression between variables P, G & T. A first regression of power output P time series variable on solar irradiance G time series has shown spurious results and thus spurious regression. The first differences of such time series are stationary and a regression is proposed whereas temperature variable is identified as not significant and where autocorrelation of residuals is suspected. Finally, the novelty of this paper is the Engle & Granger method that is used to provide a relationship between variables P and G in a difference level. A final relationship without suspicious heteroscedasticity has been determined. Our model is formulated on the basis of PV real conditions statistical approach and is more realistic than steady approach models. [ABSTRACT FROM AUTHOR]

Geographically weighted regression (GWR) is a technique that explores spatial nonstationarity in data‐generating processes by allowing regression coefficients to vary spatially. It is a widely applied technique across domains because it is intuitive and conforms to the well‐understood framework of regression. An alternative method to GWR that has been suggested is spatial filtering, which it has been argued provides a superior alternative to GWR by producing spatially varying regression coefficients that are not correlated with each other and which display less spatial autocorrelation. It is, therefore, worthwhile to examine these claims by comparing the output from both methods. We do this by using simulated data that represent two sets of spatially varying processes and examining how well both techniques replicate the known local parameter values. The article finds no support that spatial filtering produces local parameter estimates with superior properties. The results indicate that the original spatial filtering specification is prone to overfitting and is generally inferior to GWR, while an alternative specification that minimizes the mean square error (MSE) of coefficient estimates produces results that are similar to GWR. However, since we generally do not know the true coefficients, the MSE minimizing specification is impractical for applied research. [ABSTRACT FROM AUTHOR]

An important issue is that the respiratory mortality may be a result of air pollution which can be measured by the following variables: temperature, relative humidity, carbon monoxide, sulfur dioxide, nitrogen dioxide, hydrocarbons, ozone, and particulates. The usual way is to fit a model using the ordinary least squares regression, which has some assumptions, also known as Gauss-Markov assumptions, on the error term showing white noise process of the regression model. However, in many applications, especially for this example, these assumptions are not satisfied. Therefore, in this study, a quantile regression approach is used to model the respiratory mortality using the mentioned explanatory variables. Moreover, improved estimation techniques such as preliminary testing and shrinkage strategies are also obtained when the errors are autoregressive. A Monte Carlo simulation experiment, including the quantile penalty estimators such as lasso, ridge, and elastic net, is designed to evaluate the performances of the proposed techniques. Finally, the theoretical risks of the listed estimators are given. [ABSTRACT FROM AUTHOR]

SUMMARY This paper discusses chaotic properties of fluctuating photovoltaic generation (PV) power and reveals that PV power can be decomposed into a chaotic component having shorter periods and a long-term fluctuation component. The first step is to decompose the PV power into three components containing a long-term fluctuation component, a load frequency control (LFC) component, and an irregular fluctuation component from normalized PV power data by using periodic regression analysis. The second step is to analyze the long-term fluctuation component and the LFC component using autocorrelation function. The third step is to clarify the chaotic properties of the LFC component using Lyapunov spectrum analysis. Finally, the simulation of predicting the LFC component and the normalized PV power data is carried out. This simulation clarifies that the LFC component has chaotic properties. [ABSTRACT FROM AUTHOR]

Background: In China, dengue remains an important public health issue with expanded areas and increased incidence recently. Accurate and timely forecasts of dengue incidence in China are still lacking. We aimed to use the state-of-the-art machine learning algorithms to develop an accurate predictive model of dengue. Methodology/Principal findings: Weekly dengue cases, Baidu search queries and climate factors (mean temperature, relative humidity and rainfall) during 2011–2014 in Guangdong were gathered. A dengue search index was constructed for developing the predictive models in combination with climate factors. The observed year and week were also included in the models to control for the long-term trend and seasonality. Several machine learning algorithms, including the support vector regression (SVR) algorithm, step-down linear regression model, gradient boosted regression tree algorithm (GBM), negative binomial regression model (NBM), least absolute shrinkage and selection operator (LASSO) linear regression model and generalized additive model (GAM), were used as candidate models to predict dengue incidence. Performance and goodness of fit of the models were assessed using the root-mean-square error (RMSE) and R-squared measures. The residuals of the models were examined using the autocorrelation and partial autocorrelation function analyses to check the validity of the models. The models were further validated using dengue surveillance data from five other provinces. The epidemics during the last 12 weeks and the peak of the 2014 large outbreak were accurately forecasted by the SVR model selected by a cross-validation technique. Moreover, the SVR model had the consistently smallest prediction error rates for tracking the dynamics of dengue and forecasting the outbreaks in other areas in China. Conclusion and significance: The proposed SVR model achieved a superior performance in comparison with other forecasting techniques assessed in this study. The findings can help the government and community respond early to dengue epidemics. [ABSTRACT FROM AUTHOR]

Hybrid three-stage algorithms for identification of geofields that can yield high-quality indicators are examined. Integrable estimation techniques from the hybrid noise-resistant algorithm database are used for effective solution of geofield recovery problems with substantial measurement noise which are difficult to formulate and have multiple extremes. Fuzzy regression models are shown to lead to a multi-extremum non-convex optimization problem. An example is given of a single-extremum problem for finding a fuzzy linear regression model. [ABSTRACT FROM AUTHOR]

Background: The association of quantitative gait characteristics, such as gait variability with musculoskeletal pain is poorly understood. We aimed to examine whether gait speed and gait variability are associated with musculoskeletal pain assessed by the severity and the number of sites in community-dwelling elderly individuals.Methods: A total of 176 elderly individuals participated in this study. The wireless motion-recording sensor units were attached to the lower trunk and heel during gait, and an autocorrelation coefficient was calculated in three directions as parameters of gait variability of trunk movement. Musculoskeletal pain was assessed in two aspects: severity and the number of sites.Results: Moderate/severe pain intensity was significantly associated with slow gait speed and low AC in a mediolateral direction (P=0.024 and 0.026, respectively). Participants with musculoskeletal pain in multiple sites had significantly lower autocorrelation coefficient in mediolateral direction than did those without pain (P=0.003).Conclusions: Presence of moderate/severe pain intensity in at least one site or any-intensity pain in multiple sites is associated with slower gait speed and higher gait variability of trunk movement in well-functioning elderly individuals living in the community. Additional studies are necessary to elucidate the causal relationships between musculoskeletal pain and gait. [ABSTRACT FROM AUTHOR]

Several versions of the Stein-rule estimators of the coefficient vector in a linear regression model are proposed in the literature. In the present paper, we propose new feasible generalized Stein-rule restricted ridge regression estimators to examine multicollinearity and autocorrelation problems simultaneously for the general linear regression model, when certain additional exact restrictions are placed on these coefficients. Moreover, a Monte Carlo simulation experiment is performed to investigate the performance of the proposed estimator over the others. [ABSTRACT FROM AUTHOR]

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies. [ABSTRACT FROM AUTHOR]

Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and adhoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, aflexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. [ABSTRACT FROM AUTHOR]

Criminological theories of cross-national studies of homicide have underestimated the effects of quality governance of liberal democracy and region. Data sets from several sources are combined and a comprehensive model of homicide is proposed. Results of the spatial regression model, which controls for the effect of spatial autocorrelation, show that quality governance, human development, economic inequality, and ethnic heterogeneity are statistically significant in predicting homicide. In addition, regions of Latin America and non-Muslim Sub-Saharan Africa have significantly higher rates of homicides ceteris paribus while the effects of East Asian countries and Islamic societies are not statistically significant. These findings are consistent with the expectation of the new modernization and regional theories. [ABSTRACT FROM AUTHOR]

Visible and near-infrared (VNIR) reflectance spectroscopy is a rapid, non-destructive, and cost-effective method for predicting soil properties. Partial least squares regression (PLSR) is a common method used to predict soil properties based on VNIR reflectance spectra. However, PLSR ignores the spatial autocorrelation of soil properties and the assumption of linear regression models, in which explanatory variables and model residuals should be independently and identically distributed. In this study, PLSR, partial least squares–geographically weighted regression (PLS–GWR), partial least squares regression Kriging (PLSRK), and partial least squares–geographically weighted regression Kriging (PLS–GWRK) were constructed to predict soil organic matter (SOM) based on soil spectral reflectance. In addition, this study explores the influence of the spatial non-stationarity of explanatory variables on prediction accuracy. Among the aforementioned models, PLSR was used as a reference model; PLS–GWR considered the spatial autocorrelation of SOM and its auxiliary variables; PLSRK and PLS–GWRK considered the spatial dependence of the model residuals to ensure the usability of PLSR and PLS–GWR. A total of 256 topsoil samples (0–30 cm) were collected from Chahe Town, located in Jianghan Plain, China, and the reflectance spectra (400–2350 nm) of soil were used. The prediction capabilities of the models were evaluated using the coefficient of determination ( R 2 ), the root-mean-square error (RMSE), and the ratio of performance to inter-quartile range (RPIQ). The evaluation indices showed that PLS–GWRK was the optimal model for predicting SOM using VNIR spectra. PLS–GWRK has the lowest values of RMSE C [0.109 ln (g·kg − 1 )] and RMSE P [0.223 ln (g·kg − 1 )] and the highest values of R 2 C (0.933), R 2 P (0.653), and RPIQ (3.015). PLS–GWR result showed that the spatial dependence of SOM and principal components could improve prediction accuracy compared with the PLSR result. The result of PLSRK showed that the spatial dependence of the model residuals could influence the prediction accuracy of PLSR. The PLS–GWRK approach explicitly addressed the spatial dependency and spatial non-stationarity issues for interpolating SOM at regional scale. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the Andrews–Pregibon (AP), COVRATIO and Cook–Weisberg (CW) statistics to determine the influential observations on the confidence ellipsoids in linear regression model with correlated errors and correlated regressors. A real example and a Monte Carlo simulation study are given to detect the effects of autocorrelation coefficient and ridge parameter on the AP, COVRATIO and CW statistics. [ABSTRACT FROM AUTHOR]

An extended least squares method for robust, angle-independent 2-D vector velocity estimation using plane-wave ultrasound imaging is presented. The method utilizes a combination of least squares regression of Doppler autocorrelation estimates and block matching to obtain aliasing-resistant vector velocity estimates. It is shown that the aliasing resistance of the technique may be predicted using a single parameter, which is dependent on the selected transmit and receive steering angles. This parameter can therefore be used to design the aliasing-resistant transmit–receive setups. Furthermore, it is demonstrated that careful design of the transmit–receive steering pattern is more effective than increasing the number of Doppler measurements to obtain robust vector velocity estimates, especially in the presence of higher order aliasing. The accuracy and robustness of the method are investigated using the realistic simulations of blood flow in the carotid artery bifurcation, with velocities up to five times the Nyquist limit. Normalized root-mean-square (rms) errors are used to assess the performance of the technique. At −5 dB channel data blood SNR, rms errors in the vertical and horizontal velocity components were approximately 5% and 15% of the maximum absolute velocity, respectively. Finally, the in vivo feasibility of the technique is shown by imaging the carotid arteries of healthy volunteers. [ABSTRACT FROM AUTHOR]

Polymeric micelles are a type of complex chemical product with multiple phases and components, and polymeric molecular structures are among the main factors influencing the micellar properties. In this study, based on block unit autocorrelation (BUA) descriptors, we employed a genetic function approximation (GFA) algorithm and multiple linear regression (MLR) to develop quantitative structure–property relationship (QSPR) models between the multi-topological structures of polymers and micellar properties including drug loading capacity (LC) and critical micelle concentration (CMC), generating an LC optimization model with five descriptors ( n = 60, R 2 = 0.813, Q 2 LOO-CV = 0.663, Q 2 5 -fold = 0.636, F = 46.880 ( p < 0.001), Q 2 ext = 0.830, Q 2 y-rand = 0.0004) and a CMC optimization model with six descriptors ( n = 22, R 2 = 0.897, Q 2 LOO-CV = 0.702, F = 21.765 ( p < 0.001), Q 2 ext = 0.717, Q 2 y-rand = 0.0009). Based on the model analysis, the factors mainly influencing LC are the lowest unoccupied molecular orbital (LUMO) energy, dipole, electrostatic energy and electronic energy, which are related to the electronic energy level, electron distribution and interaction of electrons in molecules. The main factors affecting CMC are the energies of interactions between polymers and water, charges and branching of polymer structures. The conclusions obtained may help establish the regulatory mechanism between polymer structures and micellar properties and offer guidance for the design and development of polymeric carrier materials. [ABSTRACT FROM AUTHOR]

SUMMARY In the field of cell biology, particle counting in intracellular images is important for investigating the cause of diseases. However, particles are manually counted by human observers now. Such manually counting takes a lot of time, and counting result becomes subjective. If an automatic counting method by computer is realized, we can treat a large number of images and it can obtain many objective data. The development of an automatic counting method much contributes to understand the case of disease. However, particle counting in intracellular images by a computer is new research field, and conventional methods are little. Thus, we propose counting method based on regression analysis. We use partial least squares regression and auto-correlation between two different types of features using mask patterns for higher-order local autocorrelation feature. The proposed method gives higher accuracy than counting by principal component regression, support vector regression and ImageJ. In experiment, the proposed method can count with small error in comparison with human counting. The effectiveness of our method is shown by experiments. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the cross validation measures, namely OCV, GCV and Cp under the linear regression models when the error structure is autocorrelated and regressor data are correlated. The best performed ridge regression estimator is obtained by getting the optimal ridge parameter so as to minimize these measures. A Monte Carlo simulation study is given to see how the optimal ridge parameter is affected by autocorrelation and the strength of multicollinearity. [ABSTRACT FROM PUBLISHER]

Stock price prediction is an important and challenging problem in stock market analysis. Existing prediction methods either exploit autocorrelation of stock price and its correlation with the supply and demand of stock, or explore predictive indictors exogenous to stock market. In this paper, using transaction record of stocks with identifier of traders, we introduce an index to characterize market confidence, i.e., the ratio of the number of traders who is active in two successive trading days to the number of active traders in a certain trading day. Strong Granger causality is found between the index of market confidence and stock price. We further predict stock price by incorporating the index of market confidence into a neural network based on time series of stock price. Experimental results on 50 stocks in two Chinese Stock Exchanges demonstrate that the accuracy of stock price prediction is significantly improved by the inclusion of the market confidence index. This study sheds light on using cross-day trading behavior to characterize market confidence and to predict stock price. [ABSTRACT FROM AUTHOR]