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Linear mixed models are commonly used in analyzing stepped-wedge cluster randomized trials. A key consideration for analyzing a stepped-wedge cluster randomized trial is accounting for the potentially complex correlation structure, which can be achieved by specifying random-effects. The simplest random effects structure is random intercept but more complex structures such as random cluster-by-period, discrete-time decay, and more recently, the random intervention structure, have been proposed. Specifying appropriate random effects in practice can be challenging: assuming more complex correlation structures may be reasonable but they are vulnerable to computational challenges. To circumvent these challenges, robust variance estimators may be applied to linear mixed models to provide consistent estimators of standard errors of fixed effect parameters in the presence of random-effects misspecification. However, there has been no empirical investigation of robust variance estimators for stepped-wedge cluster randomized trials. In this article, we review six robust variance estimators (both standard and small-sample bias-corrected robust variance estimators) that are available for linear mixed models in R, and then describe a comprehensive simulation study to examine the performance of these robust variance estimators for stepped-wedge cluster randomized trials with a continuous outcome under different data generators. For each data generator, we investigate whether the use of a robust variance estimator with either the random intercept model or the random cluster-by-period model is sufficient to provide valid statistical inference for fixed effect parameters, when these working models are subject to random-effect misspecification. Our results indicate that the random intercept and random cluster-by-period models with robust variance estimators performed adequately. The CR3 robust variance estimator (approximate jackknife) estimator, coupled with the number of clusters minus two degrees of freedom correction, consistently gave the best coverage results, but could be slightly conservative when the number of clusters was below 16. We summarize the implications of our results for the linear mixed model analysis of stepped-wedge cluster randomized trials and offer some practical recommendations on the choice of the analytic model. [ABSTRACT FROM AUTHOR]

We propose the "Marshall–Olkin Bivariate Weibull Model with Modified Singularity MOBW- μ ", which focuses on bivariate distributions essential for reliability and survival analyses. Distributions such as the Marshall–Olkin bivariate exponential (MOBE) and the Marshall–Olkin bivariate Weibull (MOBW) are discussed. The MOBW- μ model is introduced, which incorporates a lag parameter μ in the singular part, and probabilistic properties such as the joint survival function, marginal density functions, and the bivariate hazard rate function are explored. In addition, aspects such as the correlation structure and survival copulation are addressed and we show that the correlation of the MOBW- μ is always lower than that of its copula, regardless of the parameters. The latter result implies that the MOBW- μ does not have the Lancaster's phenomenon that explains that any nonlinear transformation of variables decreases the correlation in absolute value. The article concludes by presenting a robust theoretical framework applicable to various disciplines. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the reaction-diffusion equation subject to Dirichlet and Neumann boundary conditions where the input function on the boundary is randomly fluctuated. First we study the fundamental case when this function is a white noise. Explicit form of the correlation function is derived for the reaction-diffusion equation in a half-plane. In this case we obtain the Karhunen–Loève expansion (KL) of the solution which is a partially homogeneous random field, i.e., it is homogeneous along the horizontal direction, and is inhomogeneous in the vertical direction. Then, based on this representation, we extend this result to the general case when the function prescribed on the boundary is an arbitrary homogeneous random field. [ABSTRACT FROM AUTHOR]

The study proposes a two-step hybrid methodology for sparse generalized estimation equations modeling of the drivers of shareholder value creation. Through the methodology, the validity of the Gordon constant growth model is established and other non-dividend factors’ contribution to shareholder value creation is assessed. The two-step hybrid method involves picking out the right intra-subject correlation matrix and set of regressors using EAIC and QIC respectively (EAIC-QIC) and then obtaining the penalized GEE estimators of the selected model. Penalization is useful in removing redundant regressors from the final model. The performance of the proposed method was compared to that of exclusively using QIC method in selecting both the correlation matrix and set of regressors. The study results showed that, whereas EAIC preferred the parsimonious order one auto-aggressive {AR(1)} structure for the data, QIC preferred the unstructured matrix which estimates the highest number of correlation parameters. Using the AR(1) structure and Algorithm 2, the GEE model chosen had higher efficiency compared to when QIC is used to select both the correlation matrix and regressors. Based on the results, the study concludes that adopting hybrid methods enhances efficiency of GEE estimators. On firm value, the study concludes that besides the elements in the Gordon-Constant growth model, the financial health of a firm is a vital indicator of value creation ability by firms. [ABSTRACT FROM AUTHOR]

This study presents a novel statistical and computational approach using nonparametric regression, which capitalizes on correlation structure to deal with the high-dimensional data often found in pharmacogenomics, for instance, in Crohn's inflammatory bowel disease. The empirical correlation between the test statistics, investigated via simulation, can be used as an estimate of noise. The theoretical distribution of −log10(p-value) is used to support the estimation of that optimal bandwidth for the model, which adequately controls type I error rates while maintaining reasonable power. Two proposed approaches, involving normal and Laplace-LD kernels, were evaluated by conducting a case-control study using real data from a genome-wide association study on Crohn's disease. The study successfully identified single nucleotide polymorphisms on the NOD2 gene associated with the disease. The proposed method reduces the computational burden by approximately 33% with reasonable power, allowing for a more efficient and accurate analysis of genetic variants influencing drug responses. The study contributes to the advancement of statistical methodology for analyzing complex genetic data and is of practical advantage for the development of personalized medicine. [ABSTRACT FROM AUTHOR]

We propose the “Marshall–Olkin Bivariate Weibull Model with Modified Singularity MOBW-μ”, which focuses on bivariate distributions essential for reliability and survival analyses. Distributions such as the Marshall–Olkin bivariate exponential (MOBE) and the Marshall–Olkin bivariate Weibull (MOBW) are discussed. The MOBW-μ model is introduced, which incorporates a lag parameter μ in the singular part, and probabilistic properties such as the joint survival function, marginal density functions, and the bivariate hazard rate function are explored. In addition, aspects such as the correlation structure and survival copulation are addressed and we show that the correlation of the MOBW-μ is always lower than that of its copula, regardless of the parameters. The latter result implies that the MOBW-μ does not have the Lancaster’s phenomenon that explains that any nonlinear transformation of variables decreases the correlation in absolute value. The article concludes by presenting a robust theoretical framework applicable to various disciplines.

Abstract Background Standard stepped wedge trials, where clusters switch from the control to the intervention condition in a staggered manner, can be costly and burdensome. Recent work has shown that the amount of information contributed by each cluster in each period differs, with some cluster-periods contributing a relatively small amount of information. We investigate the patterns of the information content of cluster-period cells upon iterative removal of low-information cells, assuming a model for continuous outcomes with constant cluster-period size, categorical time period effects, and exchangeable and discrete-time decay intracluster correlation structures. Methods We sequentially remove pairs of “centrosymmetric” cluster-period cells from an initially complete stepped wedge design which contribute the least amount of information to the estimation of the treatment effect. At each iteration, we update the information content of the remaining cells, determine the pair of cells with the lowest information content, and repeat this process until the treatment effect cannot be estimated. Results We demonstrate that as more cells are removed, more information is concentrated in the cells near the time of the treatment switch, and in “hot-spots” in the corners of the design. For the exchangeable correlation structure, removing the cells from these hot-spots leads to a marked reduction in study precision and power, however the impact of this is lessened for the discrete-time decay structure. Conclusions Removing cluster-period cells distant from the time of the treatment switch may not lead to large reductions in precision or power, implying that certain incomplete designs may be almost as powerful as complete designs.

Spectroscopic peak parameters are important since they provide information about the analyte under study. Besides obtaining these parameters, peak fitting also resolves overlapped peaks. Thus, the obtained parameters should permit the construction of a higher-resolution version of the original spectrum. However, peak fitting is not an easy task due to computational reasons and because the true nature of the analyte is often unknown. These difficulties are major impediments when large hyperspectral data sets need to be processed rapidly, such as for manufacturing process control. We have developed a novel and relatively fast two-part algorithm to perform peak fitting and resolution enhancement on such data sets. In the first part of the algorithm, estimates of the total number of bands and their parameters were obtained from a representative spectrum in the data set, using a combination of techniques. Starting with these parameter estimates, all the spectra were then iteratively and rapidly fitted with Gaussian bands, exploiting intrinsic features of the Gaussian distribution with vector operations. The best fits for each spectrum were retained. By reducing the obtained bandwidths and commensurately increasing their amplitudes, high-resolution spectra were constructed that greatly improved correlation-based analyses. We tested the performance of the algorithm on synthetic spectra to confirm that this method could recover the ground truth correlations between highly overlapped peaks. To assess effective peak resolution, the method was applied to low-resolution spectra of glucose and compared to results from high-resolution spectra. We then processed a larger spectral data set from mammalian cells, fixed with methanol or air drying, to demonstrate the resolution enhancement of the algorithm on complex spectra and the effects of resolution-enhanced spectra on two-dimensional correlation spectroscopy and principal component analyses. The results indicated that the algorithm would allow users to obtain high-resolution spectra relatively fast and permit the recovery of important aspects of the data's intrinsic correlation structure. Graphical Abstract This is a visual representation of the abstract. [ABSTRACT FROM AUTHOR]

Background: Standard stepped wedge trials, where clusters switch from the control to the intervention condition in a staggered manner, can be costly and burdensome. Recent work has shown that the amount of information contributed by each cluster in each period differs, with some cluster-periods contributing a relatively small amount of information. We investigate the patterns of the information content of cluster-period cells upon iterative removal of low-information cells, assuming a model for continuous outcomes with constant cluster-period size, categorical time period effects, and exchangeable and discrete-time decay intracluster correlation structures. Methods: We sequentially remove pairs of "centrosymmetric" cluster-period cells from an initially complete stepped wedge design which contribute the least amount of information to the estimation of the treatment effect. At each iteration, we update the information content of the remaining cells, determine the pair of cells with the lowest information content, and repeat this process until the treatment effect cannot be estimated. Results: We demonstrate that as more cells are removed, more information is concentrated in the cells near the time of the treatment switch, and in "hot-spots" in the corners of the design. For the exchangeable correlation structure, removing the cells from these hot-spots leads to a marked reduction in study precision and power, however the impact of this is lessened for the discrete-time decay structure. Conclusions: Removing cluster-period cells distant from the time of the treatment switch may not lead to large reductions in precision or power, implying that certain incomplete designs may be almost as powerful as complete designs. [ABSTRACT FROM AUTHOR]

The Interpretable Components (IC) use restrictions in order to have a better interpretation of the coefficients related to a Principal Component (PC). The efficiency of a (IC) due to a (PC) is made in relation to the angle formed between the Components, it being desirable the lowest value. In this context, an alternative to enrich this validation is the use of measures and circular distances so far not applied for this purpose. Given this motivation, this paper aims to propose the use of these measures to evaluate the robustness of the (IC) compared to samples contaminated with outliers, using measures and circular distances. According to various scenarios evaluated through Monte Carlo simulation, it was concluded that the use of these measures are recommended to validate the (PC) and when considering the Toeplitz correlation structure, IC were more robust in relation to the presence of outliers. [ABSTRACT FROM AUTHOR]

The occurrence of missing observations is nearly unavoidable in longitudinal studies where repeated measurements are taken over time on the same subject who may miss appointments or drop out during the study period. In this article, we use the Gaussian estimating objective function to estimate the regression and correlation parameters and handle missing data using multiple imputation. The estimation of these parameters is carried out simultaneously using the iterative Newton-Raphson algorithm and the expectation-maximization algorithm. These ideas are implemented using two real data sets and both algorithms showed comparable results with respect to the standard errors of the parameters of interest. [ABSTRACT FROM AUTHOR]

It is known that both the morphofunctional indicators and the level of development of specific physical qualities have a huge influence on the sports achievement in basketball. Their values determine the extent to which the genetic predisposition of each competitor combined with his technical-tactical preparation will be realized in the training and especially in the competition activity. It has also been proven that the complex development of motor skills in primary education is extremely important in laying the foundations for sports specialization at a later stage. There fore, in the present study we apply a correlation analysis, through which to establish the presence of relationships between two or more variables and to estimate the degree of dependence between the variables. The purpose of the study is to establish and compare the changes that occurred in the correlation structure of physical development, physical performance, specific preparedness and some mental qualities in 15-16-year-old basketball players after an applied model of basketball training. To achieve the goal, the following tasks were set: 1. To establish the correlation structures of physical development, physical capacity, specific preparedness and some mental qualities in the two studied groups. 2. To analyze the correlation-structural models of the experimental and control groups. The object of the research is the physical development, physical capacity, specific preparation and some mental qualities of the 15-16-year-old female basketball players. The subject of the experiment is the influence of the basketball training model on 15-16-year-old female basketball players. The contingent of the study are 15-16-year-old female basketball players, distributed in equal number - 15 in each group. The experimental group includes 15 basketball players from BC "Rositsa", Pavlikeni, who work according to a developed basketball training model, three times a week. The control group consists of 15 girls from "Bacho Kiro" Secondary School, Pavlikeni, who practice basketball, also three times a week. The research was conducted within one academic and training year. According to some authors, the relationship between height, weight and BMI is logical, which is confirmed by their persistence after cessation of exposure to a large and extremely large degree. In a study by M. TsankovaKaloyanova and G. Tomov among female basketball players of the same age studied, it was found that the signs "Running between stances" and "Running - shuttle" are included in the most addictions, which carry information about the level of development of speed endurance. The emergence of these significant and moderate dependencies is due, in our opinion, to the application of various effective basketball training models. [ABSTRACT FROM AUTHOR]

This study presents a novel statistical and computational approach using nonparametric regression, which capitalizes on correlation structure to deal with the high-dimensional data often found in pharmacogenomics, for instance, in Crohn’s inflammatory bowel disease. The empirical correlation between the test statistics, investigated via simulation, can be used as an estimate of noise. The theoretical distribution of −log10(p-value) is used to support the estimation of that optimal bandwidth for the model, which adequately controls type I error rates while maintaining reasonable power. Two proposed approaches, involving normal and Laplace-LD kernels, were evaluated by conducting a case-control study using real data from a genome-wide association study on Crohn’s disease. The study successfully identified single nucleotide polymorphisms on the NOD2 gene associated with the disease. The proposed method reduces the computational burden by approximately 33% with reasonable power, allowing for a more efficient and accurate analysis of genetic variants influencing drug responses. The study contributes to the advancement of statistical methodology for analyzing complex genetic data and is of practical advantage for the development of personalized medicine.

Portfolio optimization approaches inevitably rely on multivariate modeling of markets and the economy. In this paper, we address three sources of error related to the modeling of these complex systems: 1. oversimplifying hypothesis; 2. uncertainties resulting from parameters' sampling error; 3. intrinsic non-stationarity of these systems. For what concerns point 1. we propose a L 0 -norm sparse elliptical modeling and show thatsparsification is effective. We quantify the effects of points 2. and 3. by studying the models' likelihood in- and out-of-sample for parameters estimated over different train windows. We show that models with larger off-sample likelihoods lead to better performing portfolios only for shorter train sets. For larger train sets, we found that portfolio performances deteriorate and detaches from the models' likelihood, highlighting the role of non-stationarity. Investigating the out-of-sample likelihood of individual observations we show that the system changes significantly through time. Larger estimation windows lead to stable likelihood in the long run, but at the cost of lower likelihood in the short term: the "optimal" fit in finance needs to be defined in terms of the holding period. Lastly, we show that sparse models outperform full-models and conventional GARCH extensions by delivering higher out of sample likelihood, lower realized volatility and improved stability, avoiding typical pitfalls of conventional portfolio optimization approaches. [ABSTRACT FROM AUTHOR]

The results of a study of the population structure of biochemical features (a large number of volatile needle terpenoids) on large samples of Scots pine trees are presented. Data were analyzed using correlation, cluster, and principal component analysis. Significant conjugation of the content of all isolated needle compounds was shown. Features of the correlation structure of terpenoids indicate that the processes of their group synthesis can be simultaneously triggered in plants. It is concluded that it is possible to use static data obtained on large samples of trees for a preliminary study of the processes of interconversions of terpenoid compounds in coniferous plants, which are characterized by high reactivity and the complexity of their study by chemical methods. [ABSTRACT FROM AUTHOR]

Longitudinal metagenomics has been widely studied in the recent decade to provide valuable insight for understanding microbial dynamics. The correlation within each subject can be observed across repeated measurements. However, previous methods that assume independent correlation may suffer from incorrect inferences. In addition, methods that do account for intra-sample correlation may not be applicable for count data. We proposed a distribution-free approach, namely CorrZIDF, which extends the current method to model correlated zero-inflated metagenomic count data, offering a powerful and accurate solution for detecting significance features. This method can handle different working correlation structures without specifying each margin distribution of the count data. Through simulation studies, we have shown the robustness of CorrZIDF when selecting a working correlation structure for repeated measures studies to enhance the efficiency of estimation. We also compared four methods using two real datasets, and the new proposed method identified more unique features that were reported previously on the relevant research. [ABSTRACT FROM AUTHOR]

Background: When designing and analysing longitudinal cluster randomised trials, such as the stepped wedge, the similarity of outcomes from the same cluster must be accounted for through the choice of a form for the within-cluster correlation structure. Several choices for this structure are commonly considered for application within the linear mixed model paradigm. The first assumes a constant intra-cluster correlation for all pairs of outcomes from the same cluster (the exchangeable/Hussey and Hughes model); the second assumes that correlations of outcomes measured in the same period are higher than outcomes measured in different periods (the block exchangeable model) and the third is the discrete-time decay model, which allows the correlation between pairs of outcomes to decay over time. Currently, there is limited guidance on how to select the most appropriate within-cluster correlation structure. Methods: We simulated continuous outcomes under each of the three considered within-cluster correlation structures for a range of design and parameter choices, and, using the ASReml-R package, fit each linear mixed model to each simulated dataset. We evaluated the performance of the Akaike and Bayesian information criteria for selecting the correct within-cluster correlation structure for each dataset. Results: For smaller total sample sizes, neither criteria performs particularly well in selecting the correct within-cluster correlation structure, with the simpler exchangeable model being favoured. Furthermore, in general, the Bayesian information criterion favours the exchangeable model. When the cluster auto-correlation (which defines the degree of dependence between observations in adjacent time periods) is large and number of periods is small, neither criteria is able to distinguish between the block exchangeable and discrete time decay models. However, for increasing numbers of clusters, periods, and subjects per cluster period, both the Akaike and Bayesian information criteria perform increasingly well in the detection of the correct within-cluster correlation structure. Conclusions: With increasing amounts of data, be they number of clusters, periods or subjects per cluster period, both the Akaike and Bayesian information criteria are increasingly likely to select the correct correlation structure. We recommend that if there are sufficient data available when planning a trial, that the Akaike or Bayesian information criterion is used to guide the choice of within-cluster correlation structure in the absence of other compelling justifications for a specific correlation structure. We also suggest that researchers conduct supplementary analyses under alternate correlation structures to gauge sensitivity to the initial choice. [ABSTRACT FROM AUTHOR]

We study topology of correlation structures and construct Pearson correlation-based networks (MST-Pearson) and partial correlation-based networks (MST-Partial) during two time periods of extreme terrorist activities (High civilian and security forces fatalities) and relaxed period (low civilian and security forces fatalities). Our results find that probability density function of Pearson correlation coefficients for relaxed period and partial correlation coefficients for both periods slightly deviates from the gaussian function. MST-Pearson during the period of extreme terrorist activities is a crisis like less stable market structure in comparison with the meta-stable market state structure of relaxed period. Our studies also find presence of two most prominent clusters belonging to cement, and chemical and pharmaceutical sectors among four MSTs. In addition, we find important role of few sectors during the period of extreme terrorist activities in comparison with a more diversified sectoral role in the relaxed period. Furthermore, time varying topological properties indicate an expansion in both MST-Pearson and MST-Partial length in the relaxed period due to counter terrorism strategies. Thus, the study reveals interesting findings and implications for the policymakers and investors of Pakistan stock market during the event of terrorism.

A force plate is one of the most popular tools for postural stability assessment. It decomposes the ground reaction force (GRF) applied to the human body into multiple force components to determine the center of pressure (COP), which is the point at which the GRF is applied. Many COP measures have been proposed to characterize postural stability. Despite postural stability being closely related to GRF components, the interactions between them have rarely been studied. By studying the correlation structure of these GRF components, we developed a set of features to assess postural stability. We determined the correlation matrix of these GRF components and subsequently solved the corresponding eigenvalue problem; we used the resulting eigenvalues to characterize postural stability. The effectiveness of the proposed features was demonstrated by using them to differentiate between individuals in two age groups: 18–24 and 65–73 years. Statistical test results showed that the correlation matrix eigenvalues of the two age groups differed significantly. The classification results demonstrated that most of the correlation matrix eigenvalues were more sensitive to age variations than one of the most reliable and accurate conventional COP features. Furthermore, by reducing the force sensing requirement from three-dimensional to one-dimensional by considering only the vertical GRF components, a simplified version of the proposed approach can be obtained, which could reduce the cost of the force plate system substantially.

Copy number variation has been identified as a major source of genomic variation associated with disease susceptibility. With the advent of whole-exome sequencing (WES) technology, massive WES data have been generated, allowing for the identification of copy number variants (CNVs) in the protein-coding regions with direct functional interpretation. We have previously shown evidence of the genomic correlation structure in array data and developed a novel chromosomal breakpoint detection algorithm, LDcnv, which showed significantly improved detection power through integrating the correlation structure in a systematic modeling manner. However, it remains unexplored whether the genomic correlation exists in WES data and how such correlation structure integration can improve the CNV detection accuracy. In this study, we first explored the correlation structure of the WES data using the 1000 Genomes Project data. Both real raw read depth and median-normalized data showed strong evidence of the correlation structure. Motivated by this fact, we proposed a correlation-based method, CORRseq, as a novel release of the LDcnv algorithm in profiling WES data. The performance of CORRseq was evaluated in extensive simulation studies and real data analysis from the 1000 Genomes Project. CORRseq outperformed the existing methods in detecting medium and large CNVs. In conclusion, it would be more advantageous to model genomic correlation structure in detecting relatively long CNVs. This study provides great insights for methodology development of CNV detection with NGS data. [ABSTRACT FROM AUTHOR]

For direct statistical analysis of 3‐D structures against lateral earthquake shaking, stochastic simulation of fully nonstationary bi‐directional ground motions is essential. The recorded bi‐directional ground motions (or their projections) along the two orthogonal axes of a structure are usually correlated and their correlation influences the overall structural response. Further, the correlation is, in general, frequency‐dependent, that is, the correlation coefficients are different for different narrow frequency bands of the (composite) pair of motions. So it is important to have a method for stochastic simulation of bi‐directional motions that can maintain a target frequency‐dependent correlation. This type of simulated ensemble of bi‐directional motions for a recording process provides a sound basis for the statistical analysis of structural response vis‐à‐vis the observed/recorded correlation. In the present paper, a Priestley process based framework is proposed to simulate bi‐directional ground motions that can emulate the frequency‐dependent correlation structure of the parent recording process while maintaining the time–frequency characteristics of the recorded bi‐directional motion. Since principal directions are frequency‐dependent, it is imperative to develop a modal combination rule for multi‐directional ground motions which can address the frequency‐dependence of principal directions. For this purpose, a new ground motion frequency‐dependent modal combination rule is also proposed. It is found that the proposed frequency‐dependent combination rule performs better than the conventional frequency‐independent one, especially when the response is dominated by some frequency bands having different individual principal directions from each other or from those of the composite pair of motions. [ABSTRACT FROM AUTHOR]

Photovoltaic (PV) systems are well known as one of the most significant sources of distributed generations in the world. Nowadays, the usage of small-scale PVs by households in residential homes has increased noticeably. The output power of PVs is associated with uncertainty, so there is a need for a practicable method to forecast the output power that can be used by households. The current article presents a feasible method to predict the power of small-scale PVs in a day-ahead pattern. This applicable model does not have the complexities of other forecasting methods and can be applied by households in general. On the other hand, power produced by PVs depends on meteorological characteristics. Meanwhile, one important point to be noted is the fact that in many models the dependency of the PVs output power on meteorological characteristics is taken into account, but the correlation among these meteorological features is neglected. Therefore, in this article, the copula is used in order to model stochastic correlation structure among meteorological characteristics, such as ambient temperature, wind speed, and solar irradiance. Subsequently, by using a mathematical model for obtaining the output power of the PVs in parallel with utilizing the Monte Carlo method the prediction is performed. Here, to study the proposed method, a PV unit of a residential home in Swanson region in New Zealand is considered. The simulation results demonstrated high accuracy of the proposed method in diverse meteorological conditions. [ABSTRACT FROM AUTHOR]

We define the delayed Lévy-driven continuous-time autoregressive process via the inverse of the stable subordinator. We derive correlation structure for the observed non-stationary delayed Lévy-driven continuous-time autoregressive processes of order p, emphasizing low orders, and we show they exhibit long-range dependence property. Distributional properties are discussed as well. [ABSTRACT FROM AUTHOR]

Clustered and multivariate survival times, such as times to recurrent events, commonly arise in biomedical and health research, and marginal survival models are often used to model such data. When a large number of predictors are available, variable selection is always an important issue when modeling such data with a survival model. We consider a Cox's proportional hazards model for a marginal survival model. Under the sparsity assumption, we propose a penalized generalized estimating equation approach to select important variables and to estimate regression coefficients simultaneously in the marginal model. The proposed method explicitly models the correlation structure within clusters or correlated variables by using a prespecified working correlation matrix. The asymptotic properties of the estimators from the penalized generalized estimating equations are established and the number of candidate covariates is allowed to increase in the same order as the number of clusters does. We evaluate the performance of the proposed method through a simulation study and analyze two real datasets for the application. [ABSTRACT FROM AUTHOR]

Generalized estimating equations (GEE) incorporate a working correlation structure that is important because the more accurately this structure reflects the true structure, the more efficiently regression parameters may be estimated. Numerous criteria have therefore been proposed to select a working structure, although no criterion will always work better than all other criteria. In practice, it will be unknown which criterion will work best. Therefore, in this manuscript we propose how to utilize information from multiple criteria. We demonstrate the benefits of our proposed approach via a simulation study in a variety of settings and then in an application example. [ABSTRACT FROM AUTHOR]

In order to leverage the information embedded in the background state and observations, covariance matrices modelling is a pivotal point in data assimilation algorithms. These matrices are often estimated from an ensemble of observations or forecast differences. Nevertheless, for many industrial applications the modelling still remains empirical based on some form of expertise and physical constraints enforcement in the absence of historical observations or predictions. We have developed two novel robust adaptive assimilation methods named Covariance Updating iTerativE and Partially Updating BLUE. These two non-parametric methods are based on different optimization objectives, both capable of sequentially adapting background error covariance matrices in order to improve assimilation results under the assumption of a good knowledge of the observation error covariances. We have compared these two methods with the standard approach using a misspecified background matrix in a shallow water twin experiments framework with a linear observation operator. Numerical experiments have shown that the proposed methods bear a real advantage both in terms of posterior error correlation identification and assimilation accuracy. [ABSTRACT FROM AUTHOR]

Beam alignment (BA) is to ensure the transmitter and receiver beams are accurately aligned to establish a reliable communication link in millimeter-wave (mmwave) systems. Existing BA methods search the entire beam space to identify the optimal transmit-receive beam pair, which incurs significant BA latency on the order of seconds in the worst case. In this paper, we develop a learning algorithm to reduce BA latency, namely Hierarchical Beam Alignment (HBA) algorithm. We first formulate the BA problem as a stochastic multi-armed bandit problem with the objective to maximize the cumulative received signal strength within a certain period. The proposed algorithm takes advantage of the correlation structure among beams such that the information from nearby beams is extracted to identify the optimal beam, instead of searching the entire beam space. Furthermore, the prior knowledge on the channel fluctuation is incorporated in the proposed algorithm to further accelerate the BA process. Theoretical analysis indicates that the proposed algorithm is asymptotically optimal. Extensive simulation results demonstrate that the proposed algorithm can identify the optimal beam with a high probability and reduce the BA latency from hundreds of milliseconds to a few milliseconds in the multipath channel, as compared to the existing BA method in IEEE 802.11ad. [ABSTRACT FROM AUTHOR]

Previous research indicates the correlation structure of gait parameters (i.e., fractal dynamics) decreases with age. This decrease is suggested to reflect a reduced capacity for locomotor adaptation in older adults. The purpose of this study was to investigate potential differences between physical activity-matched young and older adults’ fractal dynamics and gait adaptability during unperturbed and asymmetric walking, and to determine if fractal dynamics predict adaptive capacity. Fifteen young (28.9 ± 5.6 years, nine women) and 15 older (64.7 ± 2.7, nine women) adults with similar habitual physical activity levels walked at preferred speed, half of preferred speed, and asymmetrically whereby their dominant and non-dominant legs moved at preferred and half-preferred speed, respectively. Fractal correlations (scaling exponent α) of stride times were assessed through detrended fluctuation analysis, and gait adaptation to asymmetric walking on the basis of lower limb relative phase. Both cohorts displayed similar fractal dynamics at preferred speed and asymmetric walking, while older adults exhibited greater α during slow walking. Both groups exhibited comparable gait adaptation to split-belt walking based on analysis of lower limb relative phase. Fractal dynamics during preferred speed and asymmetric walking was moderately associated with gait adaptation in the young and older adult cohorts, respectively. In these activity-matched groups, there were no age-based reductions in fractal dynamics or gait adaptation, and fractal scaling α was moderately associated with gait adaptation. These findings suggest that stride time fractal dynamics and gait adaptation may be preserved in older adults who habitually perform moderate intensity physical activity.

Previous research indicates the correlation structure of gait parameters (i.e., fractal dynamics) decreases with age. This decrease is suggested to reflect a reduced capacity for locomotor adaptation in older adults. The purpose of this study was to investigate potential differences between physical activity-matched young and older adults’ fractal dynamics and gait adaptability during unperturbed and asymmetric walking, and to determine if fractal dynamics predict adaptive capacity. Fifteen young (28.9 ± 5.6 years, nine women) and 15 older (64.7 ± 2.7, nine women) adults with similar habitual physical activity levels walked at preferred speed, half of preferred speed, and asymmetrically whereby their dominant and non-dominant legs moved at preferred and half-preferred speed, respectively. Fractal correlations (scaling exponent α) of stride times were assessed through detrended fluctuation analysis, and gait adaptation to asymmetric walking on the basis of lower limb relative phase. Both cohorts displayed similar fractal dynamics at preferred speed and asymmetric walking, while older adults exhibited greater α during slow walking. Both groups exhibited comparable gait adaptation to split-belt walking based on analysis of lower limb relative phase. Fractal dynamics during preferred speed and asymmetric walking was moderately associated with gait adaptation in the young and older adult cohorts, respectively. In these activity-matched groups, there were no age-based reductions in fractal dynamics or gait adaptation, and fractal scaling α was moderately associated with gait adaptation. These findings suggest that stride time fractal dynamics and gait adaptation may be preserved in older adults who habitually perform moderate intensity physical activity. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the impact of correlation structure, prevalence and effect size on the risk prediction model by using the change in the area under the receiver operating characteristic curve (ΔAUC), net reclassification improvement (NRI), and integrated discrimination improvement (IDI). In simulation study, the dataset is generated under different correlation structures, prevalences and effect sizes. We verify the simulation results with the real-data application. In conclusion, the correlation structure between the variables should be taken into account while composing a multivariable model. Negative correlation structure between independent variables is more beneficial while constructing a model. [ABSTRACT FROM AUTHOR]

This essay performs a reliability constraint stochastic model for unit commitment problem by considering generation and transmission constraints with high wind penetration and volatility of load demands. This query is expressed as a MILP that is based on the linear direct current model. The proposed approach models uncertainty of wind generators output power, load demand fluctuations and stochastic elements outage of the system like generators and transmission lines. In this paper, stochastic interdependence between random variables like wind speed and load demand is recognized. To establish the probability distribution of these correlated random variables, Copula theory is applied. Correlation structure between wind speed of different locations and a group of loads existing in the same area is investigated and studied based on historical data. For representing these uncertainties in the stochastic unit commitment problem, possible scenarios are generated with Monte Carlo simulation method. The reliability constraints are utilized in each scenario to evaluate the feasibility of solutions from a reliability point. The introduced stochastic UC is executed on the RTS 96‐bus test system. Numerical results demonstrate the advantages of implementing stochastic programming on the UC problem by taking into account the intermittent behavior of wind energy and load inconstancy. [ABSTRACT FROM AUTHOR]

We propose a novel methodology to define, analyze and forecast market states. In our approach, market states are identified by a reference sparse precision matrix and a vector of expectation values. In our procedure, each multivariate observation is associated to a given market state accordingly to a minimization of a penalized Mahalanobis distance. The procedure is made computationally very efficient and can be used with a large number of assets. We demonstrate that this procedure is successful at clustering different states of the markets in an unsupervised manner. In particular, we describe an experiment with one hundred log-returns and two states in which the methodology automatically associates states prevalently to pre- and post-crisis periods with one state gathering periods with average positive returns and the other state periods with average negative returns, therefore discovering spontaneously the common classification of 'bull' and 'bear' markets. In another experiment, with again one hundred log-returns and two states, we demonstrate that this procedure can be efficiently used to forecast off-sample future market states with significant prediction accuracy. This methodology opens the way to a range of applications in risk management and trading strategies in the context where the correlation structure plays a central role. [ABSTRACT FROM AUTHOR]

Due to the existence of the strong correlation between microarray gene expression levels, procedures which are commonly used to select the significant genes between two or more phenotypes cannot overcome the main problems: high instability of the number of false discoveries and low power. It may be impossible to completely understand these correlations due to the complexity of the biology nature. Gordon et al. [1] proposed a new multiple testing procedure to balance type I and II errors in an optimal way. However, the correlation structure of microarray data is still the main obstacle standing in the way of various gene selection procedures. To remove this obstacle, we improved the statistical methodology by exploiting the properties associated with the low dependency of the so-called delta-sequence proposed in Klebanov et al. [4]. Our study showed a similar behavior has been observed that both the mean and the standard deviation of the number of false positives are monotonically decreasing as a function of the threshold parameter. In addition, working with pairs, we have substantial reduction in both numbers, which means we gain power and stability in our new study. [ABSTRACT FROM AUTHOR]

This paper provides a new approach to incorporating the stochastic nature of damage constitutive relations in the finite-element analysis of concrete structures. Within the framework of stochastic damage mechanics, the spatial variability of concrete was modeled as a two-scale stationary random field. At the microlevel, the damage evolution law of concrete was mapped to a random field corresponding to the microscopic fracture strain. At the macrolevel, the strength distribution of any concrete component forms a lognormally distributed random field. The connection between the two-scale random fields was established by a covariance constraint such that the scale of fluctuation of the random material property was satisfied in both scales. Taking advantage of the stochastic finite-element method, both the microscopic random damage evolution of concrete and the fluctuation of macroscopic structural responses can be numerically represented. Stochastic structural modeling and damage analyses for a conventional cantilever beam and a plane frame were carried out to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

In practice, complications can arise when constructing optimal designs for non-linear regression models. One of the major problems is when the observations are correlated, since they are taken from the same individual, object or experimental unit. When using the D-optimality criterion, it depends both on the parameter vector of the model and on the correlation structure assumed for the error term. One way to avoid this dependence is through the inclusion of a priori distributions in the D-optimality criterion. In this paper we study the effect of the choice of different a priori distributions, such as the Uniform, Gamma and Lognormal distributions in obtaining the D-optimal designs for a non-linear model, when the errors present different correlation structures. The designs are found by maximizing the approximate D-optimality criterion by the Monte Carlo method. In addition, a general methodology is proposed to find D-optimal designs for any type of non-linear model in the presence of correlated observations. Finally, it is proposed to compare the designs found by calculating the efficiencies taking as a reference design the one obtained with the a priori Uniform distribution. The methodology established in a case study is applied, and it is concluded that the designs obtained depend as much on the correlation structure as on the a priori distribution considered. [ABSTRACT FROM AUTHOR]

Abstract Monitoring an aquatic environment in aquaculture is usually carried out by controlling its physicochemical and biological parameters. The global state of the process is evaluated though the individual conditions shown in each parameter. However, the correlation structure in the data, caused by interdependence between these parameters, provides relevant information which must be controlled. Thus, the complex structure of the data requires a multivariate control method to explore both the individual and interactive effects of the environmental parameters. To achieve this goal, this paper presents a statistical method based on a Multivariate Exponentially Moving Average (MEWMA) chart to monitor the multivariate structure of an aquatic environment in aquaculture, especially in a crop of tilapia in Mozambique. The results show that the adjusted MEWMA chart is more consistent when controlling the conformity and stability of environmental parameters. Therefore, it can be considered an efficient statistical method to monitor an aquatic environment in aquaculture. Highlights • This paper presents a multivariate methodology to monitor the aquatic environment in tilapia (oreochomis mossambicus) crop tanks. • It was consisted a real study in the company Aquapesca de Moçambique • The data were analyzed through a MEWMA model in order to exploit relevant information of the process concerning the state of the aquatic environment. [ABSTRACT FROM AUTHOR]

Generalized estimating equations (GEE) is one of the most commonly used methods for regression analysis of longitudinal data, especially with discrete outcomes. The GEE method accounts for the association among the responses of a subject through a working correlation matrix and its correct specification ensures efficient estimation of the regression parameters in the marginal mean regression model. This study proposes a predicted residual sum of squares (PRESS) statistic as a working correlation selection criterion in GEE. A simulation study is designed to assess the performance of the proposed GEE PRESS criterion and to compare its performance with its counterpart criteria in the literature. The results show that the GEE PRESS criterion has better performance than the weighted error sum of squares SC criterion in all cases but is surpassed in performance by the Gaussian pseudo-likelihood criterion. Lastly, the working correlation selection criteria are illustrated with data from the Coronary Artery Risk Development in Young Adults study. [ABSTRACT FROM AUTHOR]

: The batch Markov‐modulated Poisson process (BMMPP) is a subclass of the versatile batch Markovian arrival process (BMAP), which has been widely used for the modeling of dependent and correlated simultaneous events (as arrivals, failures, or risk events). Both theoretical and applied aspects are examined in this paper. On one hand, the identifiability of the stationary BMMPPm(K ) is proven, where K is the maximum batch size and m is the number of states of the underlying Markov chain. This is a powerful result for inferential issues. On the other hand, some novelties related to the correlation and autocorrelation structures are provided. [ABSTRACT FROM AUTHOR]

The spatial fluctuation of material properties is commonly modeled using random fields. However, descriptions of random fields in terms of marginal distributions and correlation structure are actually incomplete. The copulas that specify the dependence structure underlying the joint probability distribution over random fields are not provided and a Gaussian dependence structure is assumed without proper validation in practice. This study, therefore, tests the fitness of several non-Gaussian dependence structures in addition to the common use of the Gaussian dependence structure. A soil profile of cone penetration test (CPT) data is collected, and a pair-wise likelihood estimate approach is adopted to identify the best fit dependence structure. The results reveal that both q c and f s of the CPT profile exhibit the same non-Gaussian dependence characteristics, which challenges the Gaussian assumption. Generation of random fields with a non-Gaussian dependence structure is then proposed. Two slope examples where the spatial fluctuation of shear strength is respectively modeled using stationary and non-stationary random fields are used to investigate the deviation in failure probability due to different dependence structures. The effect of the dependence structure is non-trivial except when the random field is highly ragged or highly smooth. The results highlight the importance of copulas for dependence characterization in random fields. [ABSTRACT FROM AUTHOR]

We build an advanced offer curve in the day-ahead electricity market for wind power producers based on the multivariate (bivariate or two-dimensional) distribution of the real-time (RT) price and wind power forecasting errors. The bivariate distribution results in more profitable offers based on the conditional probability of wind power forecasting errors with respect to the RT price forecasting errors. The standard deviation of the bivariate distribution is reduced through a novel probabilistic wind power forecasting algorithm based on a parametric approach to further increase the profitability of the offer curve. In conclusion, the test of the advanced offer curve on the data sampled from the Iberian peninsula shows that the offer curve of the bivariate distribution has a higher profitability than offer curves of the marginal distribution. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this work was to build weighted correlation networks, in order to discover correlation structures and link patterns among 28 morphoagronomic traits of chili pepper related to seedling, plant, inflorescence, and fruit. Phenotypic and genotypic information of 16 Capsicum genotypes were analyzed. Correlation structures and link patterns can be easily identified in the matrices using the Fruchterman-Reingold algorithm with correlation network information. Both types of correlations showed the same general link pattern among fruit traits, with high broad-sense heritability values and high aptitude of the genotypes for agronomic and ornamental breeding. Leaf dimensions are correlated with a cluster of fruit traits. Correlation networks of chili pepper traits may increase the effectiveness of genotype selection, since both correlated traits and groups can be identified.