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This paper investigates the estimation of the additive model. The nonparametric functions in the model are approximated through B-splines, and the kernel density regression method is employed to estimate the unknown parameters. Moreover, the convergence rate of the proposed approach is established. We conducted numerical experiments and real-world data analysis to validate the theoretical properties of our proposed method. Our numerical findings indicate that our approach offers superior estimation performance compared to several existing methods for the additive model, particularly in the presence of asymmetric, multimodal, or heavy-tailed error distributions. [ABSTRACT FROM AUTHOR]

Abstract.In this article, we propose an additive model in which the random error follows a skew-normal p-order autoregressive (AR) process where the systematic component is approximated by cubic and cyclic cubic regression splines. The maximum likelihood estimators are calculated through the expectation-maximization (EM) algorithm with analytic expressions for the E and M-steps. The effective degrees of freedom concerning the non parametric component are estimated based on a linear smoother. The smoothing parameters are estimated by minimizing the Bayesian information criterion. The conditional quantile residuals are used to construct simulated confidence bands for assessing departures from the error assumptions. Also, we use the same residuals to construct graphs of the autocorrelation and partial autocorrelation functions to verify the AR structure’s adequacy for the errors. We then perform local influence analysis based on the conditional expectation of the complete-data log-likelihood function. A simulation study is carried out to evaluate the efficiency of the EM algorithm. Finally, the method is illustrated by using a real dataset of the average weekly cardiovascular mortality in Los Angeles. [ABSTRACT FROM AUTHOR]

This paper develops a model for multi-task machine learning that incorporates per-task parametric and nonparametric effects in an additive way. This allows a practitioner the flexibility of modeling the tasks in a customized manner, increasing model performance compared to other modern multi-task methods, while maintaining a high degree of model explainability. We also introduce novel methods for task diagnostics, which are based on the statistical influence of tasks on the model's performance, and propose testing methods and remedial measures for outlier tasks. Additive multi-task learning model with task diagnostics is examined on a well-known real-world multi-task benchmark dataset and shows a significant performance improvement over other modern multi-task methods. [ABSTRACT FROM AUTHOR]

Generalized linear models (GLMs) are an integral tool in ecology. Like general linear models, GLMs assume linearity, which entails a linear relationship between independent and dependent variables. However, because this assumption acts on the link rather than the natural scale in GLMs, it is more easily overlooked. We reviewed recent ecological literature to quantify the use of linearity. We then used two case studies to confront the linearity assumption via two GLMs fit to empirical data. In the first case study we compared GLMs to generalized additive models (GAMs) fit to mammal relative abundance data. In the second case study we tested for linearity in occupancy models using passerine point‐count data. We reviewed 162 studies published in the last 5 years in five leading ecology journals and found less than 15% reported testing for linearity. These studies used transformations and GAMs more often than they reported a linearity test. In the first case study, GAMs strongly out‐performed GLMs as measured by AIC in modeling relative abundance, and GAMs helped uncover nonlinear responses of carnivore species to landscape development. In the second case study, 14% of species‐specific models failed a formal statistical test for linearity. We also found that differences between linear and nonlinear (i.e., those with a transformed independent variable) model predictions were similar for some species but not for others, with implications for inference and conservation decision‐making. Our review suggests that reporting tests for linearity are rare in recent studies employing GLMs. Our case studies show how formally comparing models that allow for nonlinear relationships between the dependent and independent variables has the potential to impact inference, generate new hypotheses, and alter conservation implications. We conclude by suggesting that ecological studies report tests for linearity and use formal methods to address linearity assumption violations in GLMs. [ABSTRACT FROM AUTHOR]

In this article we develop semiparametric regression techniques for fitting partially linear additive models. The methods are for a general Hilbert-space-valued response. They use a powerful technique of additive regression in profiling out the additive nonparametric components of the models, which necessarily involves additive regression of the nonadditive effects of covariates. We show that the estimators of the parametric components are n -consistent and asymptotically Gaussian under weak conditions. We also prove that the estimators of the nonparametric components, which are random elements taking values in a space of Hilbert-space-valued maps, achieve the univariate rate of convergence regardless of the dimension of covariates. We present some numerical evidence for the success of the proposed method and discuss real data applications. for this article are available online. [ABSTRACT FROM AUTHOR]

The results of some divisions related to Brexit held in the House of Commons are investigated. In particular, a new class of mixture models with concomitant covariates is developed to identify groups of members of parliament with similar voting behaviour. The methodological novelty lies in the flexibility introduced by the use of smooth functions to model the effect of concomitant covariates on the component weights of the mixture. Results show this approach allows to quantify the effect of the age of members of parliament, as well as preferences and competitiveness in the constituencies they represent, on their position towards Brexit. [ABSTRACT FROM AUTHOR]

Abstract Modelling of solar irradiation is paramount to renewable energy management. This warrants the inclusion of additive effects to predict solar irradiation. Modelling of additive effects to solar irradiation can improve the forecasting accuracy of prediction frameworks. To help develop the frameworks, this current study modelled the additive effects using non-parametric quantile regression (QR). The approach applies quantile splines to approximate non-parametric components when finding the best relationships between covariates and the response variable. However, some additive effects are perceived as linear. Thus, the study included the partial linearly additive quantile regression model (PLAQR) in the quest to find how best the additive effects can be modelled. As a result, a comparative investigation on the forecasting performances of the PLAQR, an additive quantile regression (AQR) model and the new quantile generalised additive model (QGAM) using out-of-sample and probabilistic forecasting metric evaluations was done. Forecasted density plots, Murphy diagrams and results from the Diebold–Mariano (DM) hypothesis test were also analysed. The density plot, the curves on the Murphy diagram and most metric scores computed for the QGAM were slightly better than for the PLAQR and AQR models. That is, even though the DM test indicates that the PLAQR and AQR models are less accurate than the QGAM, we could not conclude an outright greater forecasting performance of the QGAM than the PLAQR or AQR models. However, in situations of probabilistic forecasting metric preferences, each model can be prioritised to be applied to the metric where it performed slightly the best. The three models performed differently in different locations, but the location was not a significant factor in their performances. In contrast, forecasting horizon and sample size influenced model performance differently in the three additive models. The performance variations also depended on the metric being evaluated. Therefore, the study has established the best forecasting horizons and sample sizes for the different metrics. It was finally concluded that a 20% forecasting horizon and a minimum sample size of 10000 data points are ideal when modelling additive effects of solar irradiation using non-parametric QR.

Introduction: The rapid increase in population, growth of urbanization and industrialization in recent years, which is generally associated with an increase in demand and energy consumption, and as a result, an increase in pollutant emission sources, has exacerbated air pollution as one of the biggest current crises of urban societies and consequently health risks and related social inequalities in terms of time and space. On the other hand, meteorological parameters directly affect the amount of pollutants as well as the duration of their presence in the atmosphere, and the present research was conducted in order to investigate this effect and discover the relationships between criteria air pollutants and atmospheric elements.Material and Methods: In addition to investigating the status of meteorological elements (temperature, precipitation, wind speed, relative humidity, radiation, sunshine hours and cloudiness) and air pollutants (carbon monoxide (CO), nitrogen dioxide (NO2), sulfur dioxide (SO2), ozone (O3) and particulate matters with aerodynamic diameters less than 10 microns and 2.5 microns (PM10 and PM2.5)) in Tabriz city during 2004-2021, the present study has explored the relationships between pollutants and meteorological parameters in monthly and seasonal time scales using Pearson's correlation test at the 95% confidence level and the effect of these elements on the concentration of pollutants using Multiple Linear Regression (MLR) and Generalized Additive Model (GAM) in R 4.3.1 statistical software.Results and Discussion: Based on the results of Pearson correlation analysis, NO2 and PM2.5, SO2 and PM2.5 pollutants and PM2.5 and PM10 pollutants have shown a significant positive correlation in pairs, so it seems that these pollutants have similar emission sources. Also, the results of this research demonstrate that the concentration of air pollutants in Tabriz was affected by weather conditions during the entire statistical period in the monthly and seasonal time scales. NO2 and PM2.5 pollutants had the most negative monthly correlation with the parameters of temperature, wind speed and sunshine hours and the most positive correlation with relative humidity; PM2.5 had the most positive correlation with pressure; CO and SO2 had the most negative correlation with radiation; O3 had a strong positive correlation with temperature, wind speed and sunny hours and the most negative correlation with pressure, relative humidity and cloudiness; and NO2 and PM10 pollutants had the most positive correlation with cloudiness. The results of fitting Multiple Linear Regression (MLR) and Generalized Additive Model (GAM) for each criteria in Tabriz city indicated the better performance of GAM in analyzing the relationships between all air pollutants and the set of independent variables except NO2.Conclusion: The results of this research indicate that the effect of atmospheric elements on the concentration of pollutants in Tabriz city is different depending on the type of pollutant and at different times, and it can be acknowledged that the effect of a specific meteorological parameter on air pollution is uncertain. However, wind speed, radiation, temperature and air pressure are the most important meteorological elements related to the concentration of pollutants in Tabriz city. Also, the results suggest that both MLR and GAM can describe the variability of the response variable by a set of predictor variables and explain the linear and non-linear relationships between them. However, considering the non-linear relationship between the concentration of atmospheric pollutants and meteorological elements, GAM is able to justify a higher percentage of changes in all criteria atmospheric pollutants except NO2.

Modelling of solar irradiation is paramount to renewable energy management. This warrants the inclusion of additive effects to predict solar irradiation. Modelling of additive effects to solar irradiation can improve the forecasting accuracy of prediction frameworks. To help develop the frameworks, this current study modelled the additive effects using non-parametric quantile regression (QR). The approach applies quantile splines to approximate non-parametric components when finding the best relationships between covariates and the response variable. However, some additive effects are perceived as linear. Thus, the study included the partial linearly additive quantile regression model (PLAQR) in the quest to find how best the additive effects can be modelled. As a result, a comparative investigation on the forecasting performances of the PLAQR, an additive quantile regression (AQR) model and the new quantile generalised additive model (QGAM) using out-of-sample and probabilistic forecasting metric evaluations was done. Forecasted density plots, Murphy diagrams and results from the Diebold–Mariano (DM) hypothesis test were also analysed. The density plot, the curves on the Murphy diagram and most metric scores computed for the QGAM were slightly better than for the PLAQR and AQR models. That is, even though the DM test indicates that the PLAQR and AQR models are less accurate than the QGAM, we could not conclude an outright greater forecasting performance of the QGAM than the PLAQR or AQR models. However, in situations of probabilistic forecasting metric preferences, each model can be prioritised to be applied to the metric where it performed slightly the best. The three models performed differently in different locations, but the location was not a significant factor in their performances. In contrast, forecasting horizon and sample size influenced model performance differently in the three additive models. The performance variations also depended on the metric being evaluated. Therefore, the study has established the best forecasting horizons and sample sizes for the different metrics. It was finally concluded that a 20% forecasting horizon and a minimum sample size of 10000 data points are ideal when modelling additive effects of solar irradiation using non-parametric QR. [ABSTRACT FROM AUTHOR]

We propose the t otal v ariation penalized s parse a dditive support vector m achine (TVSAM) for performing classification in the high-dimensional settings, using a mixed |$l_{1}$| -type functional regularization scheme to induce sparsity and smoothness simultaneously. We establish a representer theorem for TVSAM, which turns the infinite-dimensional problem into a finite-dimensional one, thereby providing computational feasibility. Even for the least squares loss, our result fills a gap in the literature when compared with the existing representer theorem. Theoretically, we derive some risk bounds for TVSAM under both exact sparsity and near sparsity, and with arbitrarily specified internal knots. In this process, we develop an important interpolation inequality for the space of functions of bounded variation, relying on analytic techniques such as mollification and partition of unity. An efficient implementation based on the alternating direction method of multipliers is employed. [ABSTRACT FROM AUTHOR]

We propose a novel marginal additive model (MAM) for modeling cluster‐correlated data with nonlinear population‐averaged associations. The proposed MAM is a unified framework for estimation and uncertainty quantification of a marginal mean model, combined with inference for between‐cluster variability and cluster‐specific prediction. We propose a fitting algorithm that enables efficient computation of standard errors and corrects for estimation of penalty terms. We demonstrate the proposed methods in simulations and in application to (a) a longitudinal study of beaver foraging behavior and (b) a spatial analysis of Loa loa infection in West Africa. [ABSTRACT FROM AUTHOR]

Introduction: The rapid increase in population, growth of urbanization and industrialization in recent years, which is generally associated with an increase in demand and energy consumption, and as a result, an increase in pollutant emission sources, has exacerbated air pollution as one of the biggest current crises of urban societies and consequently health risks and related social inequalities in terms of time and space. On the other hand, meteorological parameters directly affect the amount of pollutants as well as the duration of their presence in the atmosphere, and the present research was conducted in order to investigate this effect and discover the relationships between criteria air pollutants and atmospheric elements. Material and Methods: In addition to investigating the status of meteorological elements (temperature, precipitation, wind speed, relative humidity, radiation, sunshine hours and cloudiness) and air pollutants (carbon monoxide (CO), nitrogen dioxide (NO2), sulfur dioxide (SO2), ozone (O3) and particulate matters with aerodynamic diameters less than 10 microns and 2.5 microns (PM10 and PM2.5)) in Tabriz city during 2004-2021, the present study has explored the relationships between pollutants and meteorological parameters in monthly and seasonal time scales using Pearson's correlation test at the 95% confidence level and the effect of these elements on the concentration of pollutants using Multiple Linear Regression (MLR) and Generalized Additive Model (GAM) in R 4.3.1 statistical software. Results and Discussion: Based on the results of Pearson correlation analysis, NO2 and PM2.5, SO2 and PM2.5 pollutants and PM2.5 and PM10 pollutants have shown a significant positive correlation in pairs, so it seems that these pollutants have similar emission sources. Also, the results of this research demonstrate that the concentration of air pollutants in Tabriz was affected by weather conditions during the entire statistical period in the monthly and seasonal time scales. NO2 and PM2.5 pollutants had the most negative monthly correlation with the parameters of temperature, wind speed and sunshine hours and the most positive correlation with relative humidity; PM2.5 had the most positive correlation with pressure; CO and SO2 had the most negative correlation with radiation; O3 had a strong positive correlation with temperature, wind speed and sunny hours and the most nega tive correlation with pressure, relative humidity and cloudiness; and NO2 and PM10 pollutants had the most positive correlation with cloudiness. The results of fitting Multiple Linear Regression (MLR) and Generalized Additive Model (GAM) for each criteria in Tabriz city indicated the better performance of GAM in analyzing the relationships between all air pollutants and the set of independent variables except NO2. Conclusion: The results of this research indicate that the effect of atmospheric elements on the concentration of pollutants in Tabriz city is different depending on the type of pollutant and at different times, and it can be acknowledged that the effect of a specific meteorological parameter on air pollution is uncertain. However, wind speed, radiation, temperature and air pressure are the most important meteorological elements related to the concentration of pollutants in Tabriz city. Also, the results suggest that both MLR and GAM can describe the variability of the response variable by a set of predictor variables and explain the linear and non-linear relationships between them. However, considering the non-linear relationship between the concentration of atmospheric pollutants and meteorological elements, GAM is able to justify a higher percentage of changes in all criteria atmospheric pollutants except NO2. [ABSTRACT FROM AUTHOR]

This study introduces distribution-free methods to estimate interval-censored willingness-to-pay (WTP) models. The approaches proposed encompass the recovery of WTP values using an iterated conditional expectation procedure and subsequent estimation of the mean WTP using parametric and nonparametric models. Methods allow us to estimate the effects of covariates on the mean WTP and the underlying probability distribution.We employ Monte Carlo simulations to compare the performance of the estimators proposed against standard parametric and nonparametric estimators. We illustrate the estimation techniques by assessing producers' WTP for services provided by an e-marketing website that helps connect farmers with local consumers. [ABSTRACT FROM AUTHOR]

In this work, we intersect data on size‐selected particulate matter (PM) with vehicular traffic counts and a comprehensive set of meteorological covariates to study the effect of traffic on air quality. To this end, we develop an M‐quantile regression model with Lasso and Elastic Net penalizations. This allows (i) to identify the best proxy for vehicular traffic via model selection, (ii) to investigate the relationship between fine PM concentration and the covariates at different M‐quantiles of the conditional response distribution, and (iii) to be robust to the presence of outliers. Heterogeneity in the data is accounted by fitting a B‐spline on the effect of the day of the year. Analytic and bootstrap‐based variance estimates of the regression coefficients are provided, together with a numerical evaluation of the proposed estimation procedure. Empirical results show that atmospheric stability is responsible for the most significant effect on fine PM concentration: this effect changes at different levels of the conditional response distribution and is relatively weaker on the tails. On the other hand, model selection allows to identify the best proxy for vehicular traffic whose effect remains essentially the same at different levels of the conditional response distribution. [ABSTRACT FROM AUTHOR]

One may measure service quality either with additive models such as SERVQUAL, SERPERF, and two-predictor model of performance and expectation, or with multiplicative models obtained by log-transformation of variables in additive models. This paper analytically compares multiplicative models with additive models. In addition, it empirically compares predictive performance of alternative models on overall service quality and customer satisfaction with a three-way factorial design: 2 forms (additive vs. multiplicative) × 3 types (SERVQUAL vs. SERVPERF vs. two-predictor model) × 2 levels (5 dimensions vs. 22 items). The empirical comparison uses the data gathered to evaluate service quality in five service industries (Hamburger Shop, Pizza Shop, Family Restaurant, Movie Theater, and Bakery Shop) with a standard SERVQUAL questionnaire. The data set includes 1,410 respondents' evaluation of service quality. The analytical and empirical comparison shows that multiplicative models have three distinct advantages. First, multiplicative models are theoretically supported by the prospect theory and the Weber's law. Second, multiplicative models allow one to identify the optimal levels of performance and expectation maximizing overall quality or customer satisfaction. Third, multiplicative models predict overall service quality and customer satisfaction better than additive models do. [ABSTRACT FROM AUTHOR]

We introduce a generalized additive model for location, scale, and shape (GAMLSS) next of kin aiming at distribution-free and parsimonious regression modeling for arbitrary outcomes. We replace the strict parametric distribution formulating such a model by a transformation function, which in turn is estimated from data. Doing so not only makes the model distribution-free but also allows to limit the number of linear or smooth model terms to a pair of location-scale predictor functions. We derive the likelihood for continuous, discrete, and randomly censored observations, along with corresponding score functions. A plethora of existing algorithms is leveraged for model estimation, including constrained maximum-likelihood, the original GAMLSS algorithm, and transformation trees. Parameter interpretability in the resulting models is closely connected to model selection. We propose the application of a novel best subset selection procedure to achieve especially simple ways of interpretation. All techniques are motivated and illustrated by a collection of applications from different domains, including crossing and partial proportional hazards, complex count regression, nonlinear ordinal regression, and growth curves. All analyses are reproducible with the help of the tram add-on package to the R system for statistical computing and graphics. [ABSTRACT FROM AUTHOR]

In this paper, we consider feature selection in ultrahigh-dimensional additive models with heterogeneous frequency component functions. Firstly, we introduce a new concept, weighted sum of squared conditional correlations (WSSCC), which measures the correlation between a random variable and its function. Afterwards, we propose a sure independence screening procedure based on WSSCC (WSSCCSIS), whose sure screening property is established. Furthermore, a sequential feature selection procedure based on WSSCC (WSSCCFR) is proposed. Numerical studies including comprehensive simulation and a real data analysis are carried out to demonstrate the advantage of our method over other existing approaches. • We proposed a new concept WSSCC measuring the correlation between a random variable and its function. • We proposed a novel feature screening procedure WSSCCSIS and a novel feature selection procedure WSSCCFR. • Our proposed procedures are capable of handling heterogeneous component functions for ultrahigh-dimensional additive models. • We provided sufficient numerical evidences to demonstrate the advantages of our methods. [ABSTRACT FROM AUTHOR]

The wide industrial use of kaolinite requires that the extraction processes be modeled to determine the appropriate conditions of the benefit. Although classic linear regression models have been used, these have not been appropriate due to the non-compliance with normal distribution for the response variable. The data analyzed in this study correspond to a kaolinite extraction process by surface physicochemistry carried out in La Unión, Antioquia, Colombia. The response variable was the zeta potential and the explanatory variables were type of collecting solution, concentration, and pH. In this article, the recovery of kaolinite is modeled through generalized additive models, which can choose the statistical distribution and model all the parameters based on explanatory variables. Five distributions were selected for the response variable according to the Akaike information criterion (AIC). The model with generalized distribution Beta 2 was the model that presented the best performance according to the metrics used and it was found that the best-operating conditions obtained are the type of oleic acid collector, the concentration of 10 units, and pH 6. [ABSTRACT FROM AUTHOR]

This paper aims to present an overview of Semiparametric additive models. An estimation of the finite‐parameters of semiparametric regression models that involve additive nonparametric components is explained, including their historical background. In addition, three different smoothing techniques are considered in order to show the working procedures of the estimators and to explore their statistical properties: smoothing splines, kernel smoothing and local linear regression. These methods are compared with respect to both their theoretical and practical behaviors. A simulation study and a real data example are carried out to reveal the performances of the three methods. Accordingly, the advantages and disadvantages of each method regarding semiparametric additive models are presented based on their comparative scores using determined evaluation metrics for loss of information. This article is categorized under:Statistical Learning and Exploratory Methods of the Data Sciences > Modeling MethodsStatistical and Graphical Methods of Data Analysis > Multivariate AnalysisStatistical Models > Semiparametric Models [ABSTRACT FROM AUTHOR]

Nonparametric and machine learning methods are flexible methods for obtaining accurate predictions. Nowadays, data sets with a large number of predictors and complex structures are fairly common. In the presence of item nonresponse, nonparametric and machine learning procedures may thus provide a useful alternative to traditional imputation procedures for deriving a set of imputed values used next for the estimation of study parameters defined as solution of population estimating equation. In this paper, we conduct an extensive empirical investigation that compares a number of imputation procedures in terms of bias and efficiency in a wide variety of settings, including high-dimensional data sets. The results suggest that a number of machine learning procedures perform very well in terms of bias and efficiency. [ABSTRACT FROM AUTHOR]

Non-parametric, additive models are able to capture complex data dependencies in a flexible, yet interpretable way. However, choosing the format of the additive components often requires non-trivial data exploration. Here, as an alternative, we propose PrAda-net, a one-hidden-layer neural network, trained with proximal gradient descent and adaptive lasso. PrAda-net automatically adjusts the size and architecture of the neural network to reflect the complexity and structure of the data. The compact network obtained by PrAda-net can be translated to additive model components, making it suitable for non-parametric statistical modelling with automatic model selection. We demonstrate PrAda-net on simulated data, where we compare the test error performance, variable importance and variable subset identification properties of PrAda-net to other lasso-based regularization approaches for neural networks. We also apply PrAda-net to the massive U.K. black smoke data set, to demonstrate how PrAda-net can be used to model complex and heterogeneous data with spatial and temporal components. In contrast to classical, statistical non-parametric approaches, PrAda-net requires no preliminary modeling to select the functional forms of the additive components, yet still results in an interpretable model representation. [ABSTRACT FROM AUTHOR]

We present an innovative activity that uses data about LEGO sets to help students self-discover multiple linear regressions. Students are guided to predict the price of a LEGO set posted on Amazon.com (Amazon price) using LEGO characteristics such as the number of pieces, the theme (i.e., product line), and the general size of the pieces. By starting with graphical displays and simple linear regression, students are able to develop additive multiple linear regression models as well as interaction models to accomplish the task. We provide examples of student responses to the activity and suggestions for teachers based on our experiences. Supplementary materials for this article are available online.

Due to the advantages of indicating variable structure and efficient reasoning, Bayesian Networks (BN) have been widely used in data-driven soft sensor applications. However, restricted to linear and conditional Gaussian property, BN-based soft sensors rarely achieve high prediction accuracy. In this paper, an ensemble learning framework – additive dynamic Bayesian networks (ADBN) is proposed for enhanced feature learning, in which Dynamic Bayesian networks are used to learn the conditional independencies among variables and construct feature sets for the following base learners. Additional DBNs are constructed upon the residual information from the past model, to carry out feature learning to fit the residuals. The procedure is repeated and a termination rule from the perspective of feature learning is proposed to end this process, and thus the model complexity can be well restricted. The proposed method is validated on two actual industrial cases. It reveals that the ADBN feature learning method has obtained great improvements. Compared to the single DBN feature engineering method, the root mean square error (RMSE) performance has been improved by 20% and 13% on the two cases, respectively. [ABSTRACT FROM AUTHOR]

High-dimensional additive quantile regression model via penalization provides a powerful tool for analyzing complex data in many contemporary applications. Despite the fast developments, how to combine the strengths of additive quantile regression with total variation penalty with theoretical guarantees still remains unexplored. In this paper, we propose a new methodology for sparse additive quantile regression model over bounded variation function classes via the empirical norm penalty and the total variation penalty for local adaptivity. Theoretically, we prove that the proposed method achieves the optimal convergence rate under mild assumptions. Moreover, an alternating direction method of multipliers (ADMM) based algorithm is developed. Both simulation results and real data analysis confirm the effectiveness of our method. • Establish convergence rate for high-dimensional additive quantile regression with TV penalty. • Matching lower bound is shown. • Numerical results demonstrated the favorable performance. [ABSTRACT FROM AUTHOR]

This paper proposes Maximal Associated Regression (MAR), a novel algorithm that performs forward stage-wise regression by applying nonlinear transformations to fit predictor covariates. For each predictor, MAR selects between a linear or additive fit as determined by the dataset. The proposed algorithm is an adaptation of Least Angle Regression (LARS) and retains its efficiency in building sparse models. Constrained penalized splines are used to generate smooth nonlinear transformations for the additive fits. A monotonically constrained extension of MAR (MARm) is also introduced in this paper to fit isotonic regression problems. The proposed algorithms are validated on both synthetic and real datasets. The performances of MAR and MARm are compared against LARS, Generalized Linear Models (GLM), and Generalized Additive Models (GAM) under the Gaussian assumption with a unity link function. Results indicate that MAR-type algorithms achieve a superior subset selection accuracy, generating sparser models that generalize well to new data. MAR is also able to generate models for sample deficient datasets. Thus, MAR is proposed as a valuable tool for subset selection and data exploration, especially when a priori knowledge of the dataset is unavailable.

The purpose of this study was to predict seasonal time series data using the Holt-Winters exponential smoothing additive model. The data used in this study is data on the number of passengers departing at Hasanudin Airport in 2009-2019, the source of the data obtained from the official website of the Central Statistics Agency. The results showed that the Holt-Winters exponential smoothing method on the passenger's number at Hasanudin Airport in 2009 to 2019 contained trend patterns and seasonal patterns, by first determining the initial values and smoothing parameters that could minimize forecasting errors.

The increase in the number of Data Centers, in recent years, generates an increasing consumption of energy, with a considerable impact on global energy consumption and effects on the environment. Efficient energy monitoring is the foundation of building a "green" data center. A energy model for servers is required to achieve energy management in data centers. This article presents and analyzes several server energy models, more often used for data centers. The variables involved in server energy models are the frequency and degree of processor usage, memory and hard disk usage, performance, temperature, and fan speed. Server energy models are mainly classified into additive models and active-base models. A comparative analysis of server energy models and their application error is performed. Experimentally, an analysis of energy consumption for different servers was performed.

Benthic organisms play an important role in aquatic ecosystems and are often used as indicators of toxic environments. In this study, we reconstructed the spatial and temporal trend of risk to benthic communities living in sediments of the Mediterranean Sea posed by the presence of 16 polycyclic aromatic hydrocarbons (PAHs). Moreover, the origins of PAH contamination in the sea were also investigated. The analysis included multiple steps, starting with an in-depth review of available studies (from the early 1980s to 2019) reporting PAH concentrations in sediments of the Mediterranean Sea. Subsequently, the collected data were spatialised and clustered according to the four basins of the Mediterranean as defined by the Mediterranean Strategy on Sustainable Development and the United Nations Environment Programme Mediterranean Action Plan. We employed additive models, a flexible and versatile tool for coping with non-linear trends by means of smooth functions, to estimate temporal trends in PAH concentrations. Finally, the primary origins of contamination and temporal trends in ecological risk were determined using a combination of approaches. The results indicated that PAHs in Mediterranean sediments originate primarily from biomass burning, with a contribution from combustion of coal and liquid fossil fuels, the latter being representative of sites near urban centres or harbours. A significant positive correlation between annual growth rates of PAH concentration in sediment and wildfires was found. The estimated non-linear trends of concentrations and risk showed different temporal patterns across basins. In recent years, especially in the Western Mediterranean, the estimated trends suggest PAH concentrations are posing an increasing risk. These results indicate the need for stronger efforts to achieve the objectives of the Marine Strategy Framework Directive.

Path integration is a navigational strategy through which an animal remains oriented even in the absence of stable landmarks. Bump attractor networks have played a key role in modeling and analyzing the neural processes involved in path integration. In such networks, self-motion inputs and asymmetries in the network translate an activity bump over the attractor manifold, updating the animal's perceived position in space. The self-motion inputs can be incorporated through a multiplicative model, in which neuronal inputs are combined multiplicatively, or an additive model, in which neuronal inputs are combined through summation. Multiplicative models have a simple traveling wave solution and are often used to analyze properties of these networks. Relatively little mathematical analysis has been done on additive models, which are generally considered to be more biologically realistic. We analyze a general additive bump attractor model of path integration, deriving explicit mathematical expressions describing the temporal and spatial dynamics of the activity bump. We find that intrinsic spatial deformations of the activity bump lead to small, positive path integration errors that are approximately proportional to the animal's velocity. This error is minimized through a balance of acceleration and velocity input. We also derive simple expressions for the path integration gain, showing explicitly how it depends on the model parameters. Our analytical results are supported by numerical simulations of four specific, representative models. Our results have biological implications and provide a mathematical foundation for understanding a large class of path integration models. [ABSTRACT FROM AUTHOR]

A case‐crossover analysis is used as a simple but powerful tool for estimating the effect of short‐term environmental factors such as extreme temperatures or poor air quality on mortality. The environment on the day of each death is compared to the one or more "control days" in previous weeks, and higher levels of exposure on death days than control days provide evidence of an effect. Current state‐of‐the‐art methodology and software (integrated nested Laplace approximation [INLA]) cannot be used to fit the most flexible case‐crossover models to large datasets, because the likelihood for case‐crossover models cannot be expressed in a manner compatible with this methodology. In this paper, we develop a flexible and scalable modeling framework for case‐crossover models with linear and semiparametric effects which retains the flexibility and computational advantages of INLA. We apply our method to quantify nonlinear associations between mortality and extreme temperatures in India. An R package implementing our methods is publicly available. [ABSTRACT FROM AUTHOR]

We present an innovative activity that uses data about LEGO sets to help students self-discover multiple linear regressions. Students are guided to predict the price of a LEGO set posted on Amazon.com (Amazon price) using LEGO characteristics such as the number of pieces, the theme (i.e., product line), and the general size of the pieces. By starting with graphical displays and simple linear regression, students are able to develop additive multiple linear regression models as well as interaction models to accomplish the task. We provide examples of student responses to the activity and suggestions for teachers based on our experiences. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Sparse additive models have shown promising performance for classification and variable selection in high-dimensional data analysis. However, existing methods are limited to the error metric associated with hinge loss, which are sensitive to noise around the decision boundary. In this paper, we propose a new sparse additive machine with the pinball loss, called as pin-SAM, to make the model more robust to noise around the decision boundary. Theoretical analysis on the excess misclassification error is established by integrating error decomposition and concentration estimation techniques, which shows our pin-SAM can achieve the fast learning rate under appropriate parameter conditions. The empirical studies confirm the effectiveness of the proposed approach on simulated, benchmark and coronal mass ejection data. [ABSTRACT FROM AUTHOR]

In this paper we estimate the relationship between urban sprawl and a measure of air quality, namely the number of days in which the PM10 concentration exceeds safeguard limits in European Union cities. Building on a multidimensional representation of sprawl, the paper employs several indicators to account for built-up area development, population density, and residential discontinuity. The paper employs generalised additive models to disentangle the nonlinear effects in the variables and the interaction effects of the three sprawl dimensions. A significant and robust effect of urban morphology emerges after controlling for socio-economic, demographic, and climatic factors and the geographical location of the city. We find that urban sprawl impacts positively on pollutant concentration, but the effect is highly context-specific because of threshold effects and interactions. [ABSTRACT FROM AUTHOR]

Estimation of heterogeneous treatment effects is an essential component of precision medicine. Model and algorithm-based methods have been developed within the causal inference framework to achieve valid estimation and inference. Existing methods such as the A-learner, R-learner, modified covariates method (with and without efficiency augmentation), inverse propensity score weighting, and augmented inverse propensity score weighting have been proposed mostly under the square error loss function. The performance of these methods in the presence of data irregularity and high dimensionality, such as that encountered in electronic health record (EHR) data analysis, has been less studied. In this research, we describe a general formulation that unifies many of the existing learners through a common score function. The new formulation allows the incorporation of least absolute deviation (LAD) regression and dimension reduction techniques to counter the challenges in EHR data analysis. We show that under a set of mild regularity conditions, the resultant estimator has an asymptotic normal distribution. Within this framework, we proposed two specific estimators for EHR analysis based on weighted LAD with penalties for sparsity and smoothness simultaneously. Our simulation studies show that the proposed methods are more robust to outliers under various circumstances. We use these methods to assess the blood pressure-lowering effects of two commonly used antihypertensive therapies. [ABSTRACT FROM AUTHOR]

We focus on regression problems in which the predictors are naturally in the form of matrices. Reduced rank regression and related regularized method have been adapted to matrix regression. However, linear methods are restrictive in their expressive power. In this work, we consider a class of semiparametric additive models based on series estimation of nonlinear functions which interestingly induces a problem of 3rd order tensor regression with transformed predictors. Risk bounds for the estimator are derived and some simulation results are presented to illustrate the performances of the proposed method. [ABSTRACT FROM AUTHOR]

This article is concerned with the Bayesian optimal design problem for multi-factor nonlinear models. In particular, the Bayesian Ψ q -optimality criterion proposed by Dette et al. (Stat Sinica 17:463–480, 2007) is considered. It is shown that the product-type designs are optimal for the additive multi-factor nonlinear models with or without constant term when the proposed sufficient conditions are satisfied. Some examples of application using the exponential growth models with several variables are presented to illustrate optimal designs based on the Bayesian Ψ q -optimality criterion considered. [ABSTRACT FROM AUTHOR]

The whale shark is the world's largest fish that forms predictable aggregations across its range, many of which support tourism industries. The largest non-captive provisioned whale shark destination globally is at Oslob, Philippines, where more than 500 000 tourists visit yearly. There, the sharks are provisioned daily, year-round, allowing the human–shark interaction in nearshore waters. We used in-water behavioural observations of whale sharks between 2015 and 2017 to understand the relationship between external stimuli and shark behaviour, whether frequency of visits at the site can act as a predictor of behaviour, and the tourist compliance to the code of conduct. Mixed effects models revealed that the number of previous visits at the site was a strong predictor of whale shark behaviour, and that provisioned sharks were less likely to exhibit avoidance. Compliance was poor, with 93% of surveys having people less than 2 m from the animal, highlighting overcrowding of whale sharks at Oslob. Given the behavioural implications to whale sharks highlighted here and the local community's reliance on the tourism industry, it is imperative to improve management strategies to increase tourist compliance and strive for sustainable tourism practices.