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Anomaly detection is a frequently discussed topic in manufacturing. However, the issues of anomaly detection are typically attributed to the manufacturing process or equipment itself. In practice, the sensor responsible for collecting data and monitoring values may fail, leading to a biased detection result – false alarm. In such cases, replacing the sensor is necessary instead of performing equipment maintenance. This study proposes an effective framework embedded with autoencoder-based control limits that can dynamically distinguish sensor anomaly from process anomaly in real-time. We conduct a simulation numerical study and an empirical study of semiconductor assembling manufacturers to validate the proposed framework. The results show that the proposed model outperforms other benchmark methods and can successfully identify sensor failures, even under conditions of (1) large variations in process values or sensor values and (2) heteroscedasticity effect. This is particularly beneficial in various practical applications where sensors are used for numerical measurements and support equipment maintenance. [ABSTRACT FROM AUTHOR]

We investigate the nonparametric additive regression estimation in random design and long-memory errors and construct adaptive thresholding estimators based on wavelet series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function and its univariate additive components belong to Besov space. We consider the problem under two noise structures; (1) homoskedastic Gaussian long memory errors and (2) heteroskedastic Gaussian long memory errors. In the homoskedastic long-memory error case, the estimator is completely adaptive with respect to the long-memory parameter. In the heteroskedastic long-memory case, the estimator may not be adaptive with respect to the long-memory parameter unless the heteroskedasticity is of polynomial form. In either case, the convergence rates depend on the long-memory parameter only when long-memory is strong enough, otherwise, the rates are identical to those under i.i.d. errors. In addition, convergence rates are free from the curse of dimensionality. [ABSTRACT FROM AUTHOR]

Following White's approach of robust multiple linear regression [White H. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 1980;48(4):817–838], we give asymptotic confidence intervals for the multiple correlation coefficient $ R^2 $ R2 under minimal moment conditions. We also give the asymptotic joint distribution of the empirical estimators of the individual $ R^2 $ R2's. Through different sets of simulations, we show that the procedure is indeed robust (contrary to the procedure involving the near exact distribution of the empirical estimator of $ R^2 $ R2 is the multivariate Gaussian case) and can be also applied to count linear regression. Several extensions are also discussed, as well as an application to robust screening. [ABSTRACT FROM AUTHOR]

The problem of measurement error in predictors has received a vast amount of attention for both linear and non-linear models. The major focus has generally been on inference for regression coefficients, while residual analysis, variance estimation and heteroscedasticity assessment have received limited attention. In this paper we propose and evaluate new methods, based on reconstructed predictors, to address these problems in the context of linear regression. Methods using moment reconstructed predictors are found to perform well, including a new model-based bootstrapping technique for testing heteroscedasticity. Motivated by an example where the predictor is methylation rate and the measurement error model is based on the binomial distribution, particular attention is given to being able to handle the situation where both the measurement error variances and the variance of the error in the equation may be changing as a quadratic function of the unobserved predictor. [ABSTRACT FROM AUTHOR]

Estimating the long-run variance (LRV) is crucial for several econometric issues. Constructing reliable heteroskedasticity autocorrelation consistent (HAC) variance-covariance matrices and implementing efficient generalized method of moments (GMM) estimation procedures require a consistent LRV estimate. A good VARHAC estimator (HAC matrix with the spectral density at frequency zero constructed using a VAR spectral estimation) requires accurately estimating the sum of autoregressive (AR) coefficients; however, a criterion that minimizes the innovation variance does not necessarily yield the best spectral estimate. This article implements an optimal VARHAC estimator using an alternative information criterion, considering the bias in the sum of the parameters for the AR estimator of the spectral density at frequency zero. [ABSTRACT FROM AUTHOR]

In this article, we present a new one-stage multiple comparison procedure for exponential mean lifetimes with the control under heteroscedasticity including one-sided and two-sided confidence intervals by improving the coverage probability and average confidence length compared with the old one. Users can use these simultaneous confidence intervals to identify better-than-the-control, worse-than-the-control and not-much-different-from-the-control products in agriculture, stock market, pharmaceutical industries in terms of the mean lifetimes. In the end, one example is used to demonstrate the proposed procedure. [ABSTRACT FROM AUTHOR]

AbstractThis paper develops permutation versions of identification-robust tests in linear instrumental variables regression. Unlike the existing randomization and rank-based tests in which independence between the instruments and the error terms is assumed, the permutation Anderson-Rubin (AR), Lagrange Multiplier (LM) and Conditional Likelihood Ratio (CLR) tests are asymptotically similar and robust to conditional heteroskedasticity under standard exclusion restriction i.e. the orthogonality between the instruments and the error terms. Moreover, when the instruments are independent of the structural error term, the permutation AR tests are exact, hence robust to heavy tails. As such, these tests share the strengths of the rank-based tests and the wild bootstrap AR tests. Numerical illustrations corroborate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract.In the realm of mixed models, this article explores the estimation method for incorporating a mixture of distributions and addressing controlled heteroscedasticity. By relaxing the assumptions of normality and homoscedasticity, we introduce a more flexible approach to analyzing data. The article presents estimation techniques for variance components, estimable vectors, and cumulants, while also developing prediction intervals and prediction ellipsoids for future observations. A numerical example is employed to illustrate the method and compare it with traditional ANOVA and Bayesian estimation methods. The results demonstrate the superior flexibility and broader applicability of the proposed methods in diverse contexts. By extending the analysis beyond conventional assumptions, these approaches enhance the accuracy and robustness of statistical inference in mixed models. [ABSTRACT FROM AUTHOR]

Spatial homoscedasticity of the error term is commonly assumed in mixed geographically weighted regression analysis. In many practical situations, however, rarely can we know a priori whether the error term is homoscedastic or not. Therefore, it is necessary to first detect the spatial heteroscedasticity of the error term before the mixed geographically weighted regression model is used. In this paper, a statistic is constructed based on the square root of the absolute value of the residuals obtained by the two step estimation. The three moment $ \chi ^2 $ χ 2 approximation is applied to compute the p value of the test. Furthermore, simulation results show that the proposed test method has high accuracy and satisfactory power in detecting spatial heteroscedasticity, even when the model errors follow non-normal distributions. A real-world data set is analysed to demonstrate the application of the proposed test method and the paper is ended with a conclusion. [ABSTRACT FROM AUTHOR]

In ridge regression, we are often concerned with acquiring ridge estimators that lead to the smallest mean square error (MSE). In this article, we have considered the problem of ridge estimation in the presence of multicollinearity and heteroscedasticity. We have introduced a scaling factor which leads to significantly improved performance of the ridge estimators as compared to their classical counterparts. For illustration purposes, we have applied our proposed methodology to some of the popular existing ridge estimators but it can be extended to other estimators as well. We have also compared our proposed estimator with popular existing estimators dealing estimation problem in the same scenario. Extensive simulations reveal the suitability of the proposed strategy, particularly in the presence of severe multicollinearity and heteroscedasticity. A real-life application highlights that the proposed strategy has the potential to be a useful tool for data analysis in the case of collinear predictors and heteroscedastic errors. [ABSTRACT FROM AUTHOR]

Multivariate regression is a widely used technique for large-scale statistical applications. In this paper, we propose a novel method for the multivariate regression model, called multivariate weighted lasso (MWL). We consider the heteroscedasticity in the noise matrix and introduce an adjustable weight to calibrate the fitting residuals of different responses. The proposed method shows an advantage in complex multivariate regressions with heteroscedasticity. To implement the procedure, an efficient algorithm is provided based on the multivariate coordinate descent. We provide theoretical guarantees for the proposed method. Numerical simulations and financial applications are conducted using the proposed and other existing methods. The results indicate that the proposed method performs well in both variable selection and coefficient estimation. [ABSTRACT FROM AUTHOR]

This study considers an estimator for the asymptotic variance-covariance matrix in time-series quantile regression models which is robust to the presence of heteroscedasticity and autocorrelation. When regression errors are serially correlated, the conventional quantile regression standard errors are invalid. The proposed solution is a quantile analogue of the Newey-West robust standard errors. We establish the asymptotic properties of the heteroscedasticity and autocorrelation consistent (HAC) covariance matrix estimator and provide an optimal bandwidth selection rule. The quantile sample autocorrelation coefficient is biased toward zero in finite sample which adversely affects the optimal bandwidth estimation. We propose a simple alternative estimator that effectively reduces the finite sample bias. Numerical simulations provide evidence that the proposed HAC covariance matrix estimator significantly improves the size distortion problem. To illustrate the usefulness of the proposed robust standard error, we examine the impacts of the expansion of renewable energy resources on electricity prices. for this article are available online. [ABSTRACT FROM AUTHOR]

An increase in location is often accompanied by an increase in variability. Moreover, in randomized studies, the presence of heteroscedasticity can indicate a treatment effect. In these cases a location-scale test is appropriate. A common approach of a location-scale test is to use the sum of a location and a scale test statistic. In this study, we focus on one-sided location-scale tests. We introduce a one-sided Lepage-type test statistic. Since right-skewed data are common in many real-world applications, we design test statistics that are powerful also for right-skewed data. Moreover, this paper introduces both a maximum test and an adaptive test utilizing the one-sided Lepage-type test statistics. The limiting distributions of the maximum test statistics are also derived. We assess the performance of the different test statistics in various scenarios for continuous distributions through Monte Carlo simulations. Our simulation results demonstrate that the proposed new test statistics can significantly increase and stabilize statistical power, making it strong competitors to existing location-scale tests. We present practical illustrations based on example data and conclude with some final remarks. [ABSTRACT FROM AUTHOR]

AbstractData heterogeneity is a challenging issue for modern statistical data analysis. There are different types of data heterogeneity in practice. In this article, we consider potential structural changes and complicated tail distributions. There are various existing methods proposed to handle either structural changes or heteroscedasticity. However, it is difficult to handle them simultaneously. To overcome this limitation, we consider statistically and computationally efficient change point detection and localization in high-dimensional quantile regression models. Our proposed framework is general and flexible since the change points and the underlying regression coefficients are allowed to vary across different quantile levels. The model parameters, including the data dimension, the number of change points, and the signal jump size, can be scaled with the sample size. Under this framework, we construct a novel two-step estimation of the number and locations of the change points as well as the underlying regression coefficients. Without any moment constraints on the error term, we present theoretical results, including consistency of the change point number, oracle estimation of change point locations, and estimation for the underlying regression coefficients with the optimal convergence rate. Finally, we present simulation results and an application to the S&P 100 dataset to demonstrate the advantage of the proposed method. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

In one-way analysis of variance models, performing simultaneous multiple comparisons of treatment groups with a control group may be of interest. Dunnett's test is used to test such differences and assumes equal variances of the response variable for each group. This assumption is not always met even after transformation. A parametric bootstrap (PB) method is developed here for comparing multiple treatment group means against the control group with unequal variances and unbalanced data. In simulation studies, the proposed method outperformed Dunnett's test in controlling the type I error under various settings, particularly when data have heteroscedastic variance and unbalanced design. Simulations show that power is often lower for the PB method than for Dunnett's test under equal variance, balanced data, or smaller sample size, but similar to or higher than for Dunnett's test with unequal variance, unbalanced data and larger sample size. The method is applied to a dataset concerning isotope levels found in elephant tusks from various geographical areas. These data have very unbalanced group sizes and unequal variances. This example illustrates that the PB method is easy to implement and avoids the need for transforming data to meet the equal variance assumption, simplifying interpretation of results. [ABSTRACT FROM AUTHOR]

A covariate-driven random coefficient generalized conditional heteroscedasticity (GARCH) time series model with the form of the buffered autoregression (BRC-GARCH-X) for modeling financial time series data is considered. As an extension of the classical two-regime threshold process, the buffered autoregression enjoys a more flexible regime-switching mechanism. Furthermore, the main feature of this model is that the threshold variable for regime-switching is formulated as a weighted average of important auxiliary variables. The estimator for regression parameters is obtained by the quasi-maximum exponential likelihood (QMEL) estimator and the corresponding asymptotic properties are established. Moreover, a mixed portmanteau test is developed for diagnostic checking. And a reasonable method for selecting search ranges for thresholds is also proposed and simulation studies are considered. As an application, we bring attention to some features of of stock returns of SP500 which shows that our model is feasible. [ABSTRACT FROM AUTHOR]

We consider hypothesis testing in instrumental variable regression models with few included exogenous covariates but many instruments—possibly more than the number of observations. We show that a ridge-regularized version of the jackknifed Anderson and Rubin (henceforth AR) test controls asymptotic size in the presence of heteroscedasticity, and when the instruments may be arbitrarily weak. Asymptotic size control is established under weaker assumptions than those imposed for recently proposed jackknifed AR tests in the literature. Furthermore, ridge-regularization extends the scope of jackknifed AR tests to situations in which there are more instruments than observations. Monte Carlo simulations indicate that our method has favorable finite-sample size and power properties compared to recently proposed alternative approaches in the literature. An empirical application on the elasticity of substitution between immigrants and natives in the United States illustrates the usefulness of the proposed method for practitioners. [ABSTRACT FROM AUTHOR]

AbstractTesting for the autoregressive conditional heteroscedasticity (ARCH) effect is an important problem in economic and financial time series. In this article, we consider the ARCH effect test for high-dimensional time series. Our test statistic is built based on the maximum element of Spearman’s rank correlation at different lags. The bootstrap methods are used to approximate the null distribution of the proposed test statistics. We also consider the goodness-of-fit test for ARCH models by applying the test to the residuals of fitted models. Simulation results show that the proposed test statistics enjoy good properties of size in finite samples. Compared to the existing methods, the new test possesses much better power. Moreover, the test is not sensitive to the underlying distribution of the time series. The proposed method is illustrated via two real data. [ABSTRACT FROM AUTHOR]

Bootstrap is a widely applicable computational statistical method. The focus of this paper lies in developing a bootstrap method for linear mixed models under homoscedasticity violation (heteroscedasticity) in variance of errors. We assume that the form of heteroscedasticity is unknown. To generate bootstrap response data as close as possible to the actual response data, we transform the marginal residuals to ensure that the variance of the modified marginal residuals in bootstrap samples is an unbiased estimator for the variance of the response variable in the linear mixed models. The consistency is proved, implying that the parameter estimators by the proposed method are asymptotically unbiased. The simulations are conducted with varying error terms and sample sizes to show improvement of the proposed method in parameter estimation. The simulation results are compared to demonstrate that the proposed method outperforms the other considered approaches including the wild method in the heteroscedastic linear mixed models under small samples and performs competitively with the parametric method and both methods outperform the other considered methods in homoscedastic linear mixed models. The proposed bootstrap method is applied to squid data for illustration of its effectiveness. [ABSTRACT FROM AUTHOR]

In a real-world regression problem, the variance usually varies with the location, which brings difficulties in prediction of the response. Existing heteroscedastic regression methods suffer from inaccurate estimation and/or high computational complexity, and cannot be used to construct satisfactory prediction intervals for small or large data. This article focuses on the problem of constructing prediction intervals of the response under heteroscedastic regression models. We apply the reconstruction approach to parameterize the mean and variance functions as forms of kernel interpolation, and use the maximum likelihood estimation method to estimate the parameters. Our method allows a small number of parameters in the parameterization forms, and only requires low computational cost. Based on these estimators and some Bayesian modifications, we provide three classes of prediction intervals. Numerical experiments for both small and large datasets indicate that they are very competitive compared with existing heteroscedastic regression methods in terms of coverage rate and computational complexity. [ABSTRACT FROM AUTHOR]

Instead of relying on null-hypothesis significance testing (NHST), researchers are consistently advised to use effect sizes (ESs) and confidence intervals (CIs) to convey research findings. However, typical ES measures for most linear models (e.g., multiple regression) assume data normality, a condition that is often violated in behavioral research. This may lead to inaccurate interpretation of ES. In multiple regression models, Cohen's f2, R2 and R adj 2 are employed by researchers, but no study has systematically evaluated their robustness in practice. Thus, this Monte Carlo simulation study evaluates the robustness of f2, R2 and R adj 2 and the associated CIs based on manipulated levels of sample sizes, magnitudes of ESs, numbers of predictors, and data violations (i.e., heavy-tailed, skewed, contaminated, lognormal, and heteroscedastic distributions of errors). This study offers guidelines regarding how robust these ESs are so that researchers can report the most appropriate ES in their research studies. [ABSTRACT FROM AUTHOR]

The Buckley–James method for the classical accelerated failure time model has been extended to accommodate heteroscedastic survival data in two ways. The first is the weighted least squares method [Yu et al. Weighted least-squares method for right-censored data in accelerated failure time model. Biometrics. 2013;69:358–365], which estimates the heteroscedasticity nonparametrically, while the second is the local Buckley–James method [Pang et al. Local Buckley–James estimation for heteroscedastic accelerated failure time model. Stat Sin. 2015;25:863–877], which uses local Kaplan–Meier method to estimate the heteroscedasticity. However, no comparisons have been done for these two methods. Furthermore, there is no hypothesis testing procedure for this heteroscedastic accelerated failure time model. This paper is then aimed to fill these two gaps to compare the two methods theoretically and numerically with extensive simulation studies. In addition, we propose a class of hypothesis tests for the parameters to provide a complete procedure for analysing heteroscedastic survival data. Two real data examples are used for practical illustration of the comparison and the new proposed tests. [ABSTRACT FROM AUTHOR]

The analysis of means (ANOM) is a method that can compare the mean of each treatment with the overall mean. As one-way ANOVA, the conventional ANOM is not robust under unequal variances. We applied two inference procedures, single-stage and modified single-stage sampling, to solve heteroscedastic analysis of means (HANOM) under unbalanced design. Using proposed weighted average across groups, the influence of the unknown mean and variance are both eliminated. To validate the stability of HANOM under several scenarios of unequal variances and sample sizes, simulation studies of empirical type I error rate are conducted to test the quality of procedures. A real application is provided for illustrating these two procedures clearly. In addition, we build an user-friendly interface to show the results of the HANOM by using Shiny package in R software. [ABSTRACT FROM AUTHOR]

We quantify the trade-promotion effects of sharing a common currency by examining two recent episodes of official dollarization. To establish causal relationships, while avoiding the methodological criticisms of the previous literature on the issue (endogeneity and heteroskedasticity), we employ a differences-in-differences strategy that compares the pre- and post-dollarization trade flows between the United States and the two dollarizers (Ecuador and El Salvador) with the trade flows between the United States and the dollarizers' neighbours. We find that the adoption of the dollar did not bring about any significant positive trade effects. Using product-level data we find that, while a few sectors saw positive increases, those instances are scattered and not the norm. Dollarization did not lead to increases in trade of previously non-traded goods either. Finally, we do not find any trade-promotion effects between Ecuador or El Salvador and the other dollarized country in the region (Panama) or between the newly dollarized countries themselves. These findings remain valid after we perform a battery of robustness tests, including PPML estimation. [ABSTRACT FROM AUTHOR]

In recent years, there has been increased interest in modeling integer-valued time series. Many methods for time series of counts have been developed in the literature because of their wide applications to epidemiology, finance, disease modeling and environmental science. The negative binomial integer-valued generalized autoregressive conditional heteroscedasticity model is a popular one, which can deal with both over-dispersion and potential extreme observations. The accurate estimation of the parameters in the model is extremely important. We adopt the marginal likelihood to estimate the intercept parameter and maximum likelihood to estimate other parameters of the model. We conduct simulations to assess the performance of this estimation method, and compare it with that of estimating all model parameters by maximum likelihood. The results show the superiority of proposed estimation method. We use two real examples to illustrate the model's ability to fit over-dispersed data and the validity of the estimation method. [ABSTRACT FROM AUTHOR]

Given k (≥2) independent and normally distributed populations with unknown means and unknown (and possibly unequal) variances, we used the single-stage sampling procedure for multiple comparison with a control to the problem of unequal sample sizes. A simulation of the family-wise error type I was conducted to validate the quality of the procedure and a numerical example was provided for illustrating this procedure. We provided a user-friendly interface by R shiny to obtain the critical values for the practitioners. [ABSTRACT FROM AUTHOR]

In this article, we consider a matrix exponential unbalanced panel data model that allows for (i) spillover effects using matrix exponential terms, (ii) unobserved heterogeneity across entities and time, and (iii) potential heteroscedasticity in the error terms across entities and time. We adopt a likelihood based direct estimation approach in which we jointly estimate the common parameters and fixed effects. To ensure that our estimator has the standard large sample properties, we show how the score functions should be suitably adjusted under both homoscedasticity and heteroscedasticity. We define our suggested estimator as the root of the adjusted score functions, and therefore our approach can be called the M-estimation approach. For inference, we suggest an analytical bias correction approach involving the sample counterpart and plug-in methods to consistently estimate the variance-covariance matrix of the suggested M-estimator. Through an extensive Monte Carlo study, we show that the suggested M-estimator has good finite sample properties. In an empirical application, we use our model to investigate the third country effects on the U.S. outward foreign direct investment (FDI) stock at the industry level. [ABSTRACT FROM AUTHOR]

The paper introduces a semiparametric estimator of the correlations among elliptically distributed random variables invariant to any form of heteroscedasticity, robust to outliers, and asymptotically normal. Our estimator is particularly fit for financial applications as vectors of stock returns are generally well approximated by heteroskedastic processes with elliptical (conditional) distributions and heavy tails. The superiority of our estimator with respect to Pearson's sample correlation in financial applications is illustrated using simulated data and real high-frequency stock returns. Using simple exponentially weighted moving averages, we extend our estimator to the case of time-varying correlations and compare it to the popular GARCH-DCC model. We show that the two approaches have comparable performances through simulations and a simple application. However, our estimator is extremely fast to compute, computationally robust, and straightforward to implement. [ABSTRACT FROM AUTHOR]

Standard long memory models are in abundance in the literature today. Selecting the best such a model in terms of capturing key requisite features and trends in data becomes a challenge. This paper addresses the issue through a sequence of Monte Carlo experiments on simulated data and introduces an interval estimate on the asymptotic variance for the long-range dependence parameter of the entire family of standard long memory time series considered within the scope of the study. [ABSTRACT FROM AUTHOR]

We consider a non-inferiority test conducted in the three-arm trials with coefficient of variations (CV) in sample means. A procedure for this non-inferiority test is proposed based on the generalized p-value (GPV) based method under normality assumption and heteroskedasticity. We demonstrated that first, the GPV-based method outperforms the comparable alternative, the Delta method in terms of empirical sizes and powers. Second, under GPV-based method, when the population mean of groups in the trial is estimated by the sample mean with CV, the empirical sizes control the significance level better than when CV is not included, especially when the ratio of the variance of the reference group to that of the experimental group and the ratio of the variance of the placebo group to that of the experimental group are not too small and that the sample size is small. Third, when the CV is included in the sample mean, the empirical powers are always higher, regardless of the sample size and methods. Additionally, when the data violates the normality assumption, it is found that the proposed GPV-based method in conjunction with CV appear to be highly acceptable through simulation results. Finally, the proposed method is illustrated with two data examples. [ABSTRACT FROM AUTHOR]

A common problem that we encounter in linear regression models is that the error variances are not the same for all the observations, that is, there is an issue of heteroscedasticity. To avoid the adverse effects of this issue on the estimates obtained by the ordinary least squares, it is a usual practice to use the estimated weighted least squares (EWLS) method or to use some adaptive methods, especially when the form of heteroscedasticity is unknown. The current article proposes a novel Bayesian version of the EWLS estimator. The performance of the proposed estimator has been evaluated in terms of its efficiency using the Monte Carlo simulations. An example has also been included for the demonstration. [ABSTRACT FROM AUTHOR]

Multivariate repeated measures data naturally arise in clinical trials and other fields such as biomedical science, public health, agriculture, social science and so on. For data of this type, the classical approach is to conduct multivariate analysis of variance (MANOVA) based on Wilks' Lambda and other multivariate statistics, which require the assumptions of multivariate normality and homogeneity of within-cell covariance matrices. However, data being analyzed nowadays show marked departure from multivariate normality and homogeneity. This paper proposes a finite-sample test by modifying the sums of squares matrices to make them insensitive to the heterogeneity in MANOVA. The proposed test is invariant to affine transformation and robust against nonnormality. The proposed method can be used in various experimental designs, for example, factorial design and crossover design. Under various simulation settings, the proposed method outperforms the classical Doubly Multivariate Model and Multivariate Mixed Model proposed elsewhere, especially for unbalanced sample sizes with heteroscedasticity. The applications of the proposed method are illustrated with ophthalmology data in factorial and crossover designs. The proposed method successfully identified and validated a significant main effect and demonstrated that univariate analysis could be oversensitive to small but clinically unimportant interactions. [ABSTRACT FROM AUTHOR]

High-dimensional data often display heteroscedasticity. If the heteroscedasticity is neglected in the regression model, it will produce inefficient inference for the regression coefficients. Quantile regression is not only robust to outliers, but also accommodates heteroscedasticity. This paper aims to simultaneously carry out variable selection and heteroscedasticity identification for the linear location-scale model under a unified framework. We develop a regularized multiple quantile regression approach simultaneously identifying the heteroscedasticity, seeking common features of quantile coefficients and eliminating irrelevant variables. We also establish the theoretical properties of the proposed method under some regularity conditions. Simulation studies are conducted to evaluate the finite sample performance of the proposed method, showing that it is able to identify the covariates that affect the variability of the response. We further apply the proposed method to analyse the Wage data. [ABSTRACT FROM AUTHOR]

Sparse quantile regression is a useful tool for variable selection, robust estimation and heteroscedasticity treatment in high-dimensional data analysis. Due to the non-smooth of quantile loss, the computation is heavier than the least square models. In the literature, there are various numerical methods for linear quantile regression, such as ADMM developed in Gu et al. [Technometrics. 2017;60(3):319–331]. However, the computation of multivariate quantile regression has not yet been fully resolved, especially when the dimension is high. Motivated by this, we will focus on the design of fast numerical algorithms for row-sparse multivariate quantile regression model. By virtue of proximal operator and Majorize–Minimization, four smoothed algorithms are designed. For all the obtained algorithms, we analyse their convergence and the parameter selection. We conduct plenty of simulations and four real data sets analysis. Finally, we conclude that the smoothed method is faster than the non-smooth method, especially when the number of predictors is large. [ABSTRACT FROM AUTHOR]

Because of the "curse of dimensionality," high-dimensional processes present challenges to traditional multivariate statistical process monitoring (SPM) techniques. In addition, the unknown underlying distribution of and complicated dependency among variables such as heteroscedasticity increase the uncertainty of estimated parameters and decrease the effectiveness of control charts. In addition, the requirement of sufficient reference samples limits the application of traditional charts in high-dimension, low-sample-size scenarios (small n, large p). More difficulties appear when detecting and diagnosing abnormal behaviors caused by a small set of variables (i.e., sparse changes). In this article, we propose two change-point–based control charts to detect sparse shifts in the mean vector of high-dimensional heteroscedastic processes. Our proposed methods can start monitoring when the number of observations is a lot smaller than the dimensionality. The simulation results show that the proposed methods are robust to nonnormality and heteroscedasticity. Two real data examples are used to illustrate the effectiveness of the proposed control charts in high-dimensional applications. The R codes are provided online. [ABSTRACT FROM AUTHOR]

In this research, we evaluated two difference based variance estimators: one by Gasser, Sroka, and Jennen-Steinmetz, and another by Hall, Kay, and Titterington for use in partially linear models. Under various settings, we compared power of tests for heteroskedasticity, and other finite population properties of the estimators using simulation studies. We also proved that under regularity conditions, the estimator from Hall, Kay, and Titterington provides larger power of the tests for heteroskedasticity. A real example is given to illustrate the usage of the estimators. [ABSTRACT FROM AUTHOR]

In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain credibility and efficiency while producing asymptotically valid inference even when the model is incorrect. In this article we present three considerations for better practice when model-assisted inference is applied to adjust for covariates under simple or covariate-adaptive randomized trials: (a) guaranteed efficiency gain: a model-assisted method should often gain but never hurt efficiency; (b) wide applicability: a valid procedure should be applicable, and preferably universally applicable, to all commonly used randomization schemes; (c) robust standard error: variance estimation should be robust to model misspecification and heteroscedasticity. To achieve these, we recommend a model-assisted estimator under an analysis of heterogeneous covariance working model that includes all covariates used in randomization. Our conclusions are based on an asymptotic theory that provides a clear picture of how covariate-adaptive randomization and regression adjustment alter statistical efficiency. Our theory is more general than the existing ones in terms of studying arbitrary functions of response means (including linear contrasts, ratios, and odds ratios), multiple arms, guaranteed efficiency gain, optimality, and universal applicability. for this article are available online. [ABSTRACT FROM AUTHOR]

Social capital (i.e. bonding and bridging) affects food security. In Indonesia, studies have been conducted at the site level, covering households in specific provinces, districts, subdistricts, or even villages. Accordingly, this study contributes to the existing literature by employing a sample of 68,304 households across Indonesia using data from Statistics Indonesia's (BPS's) 2018 National Socioeconomic Survey (SUSENAS). Based on Lewbel's (2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models." Journal of Business and Economic Statistics 30 (1): 67–80) two-stage least squares (2SLS) regression test, the results suggest that bonding and bridging social capital positively affect food security. Specifically, bridging social capital has a more substantial influence on food security. [ABSTRACT FROM AUTHOR]

In this article we derive two simple tests for two-way ANOVA under unequal variances requiring some constraints, which cannot be solved by classical regression formulas. We do so by taking the generalized p-value approach and provide explicit formulas to handle the constraints. The first test is an extension of fiducial one-way ANOVA test, which tends to assure the intended size of the test, but tends to be conservative, and the second test reduces that drawback, but may slightly exceed the intended size of the test. The second test is also a generalized test that is numerically equivalent to the parametric bootstrap (PB) test, which contains some unintended glitches in formulas, which we will rectify. Moreover, our approach does not require good estimators of parameters as PB approach does. Hence, one can take our approach dealing with such distributions as Weibull and Gamma that are used in analysis of lifetime data in engineering and analysis of Survival data in studies of public health. By taking similar approach, researchers are also encouraged to derive generalized tests in other ANOVA applications, such as higher-way ANOVA, ANCOVA and MANOVA under heteroscedasticity, especially in Mixed Effects Model applications such as repeated measures (RM) ANOVA, where the PB approach run into difficulties. [ABSTRACT FROM AUTHOR]

In this article, a nonparametric lack-of-fit test of nonlinear regression in presence of heteroscedastic variances is proposed. We consider regression models with a discrete or continuous response variable without distributional assumptions so that the test is widely applicable. The test statistic is developed using a k-nearest neighbor augmentation defined through the ranks of the predictor variable. The asymptotic distribution of the test statistic is derived under the null and local alternatives for the case of using fixed number of nearest neighbors. The parametric standardizing rate is achieved for the asymptotic distribution of the proposed test statistic. This allows the proposed test to have faster convergence rate than most of nonparametric methods. Numerical studies show that the proposed test has good power to detect both low and high frequency alternatives even for moderate sample size. The proposed test is applied to an engineering data example. [ABSTRACT FROM AUTHOR]

A two-stage variational mode decomposition approach is explored in this article to estimate the variance function in a nonparametric heteroscedastic fixed design regression model. This estimate improves the results obtained by using variational mode decomposition in the case of smooth regression function. We noticed that the amount of improvement is depending on the smoothness of the variance function. Simulations and comparisons with the earlier methods are carried out to evaluate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract The presence of multicollinearity among predictors and heteroscedastic errors has adverse impact on the performance of ordinary least squares estimates and their covariance matrix. This article introduces modified ridge estimator, namely, the heteroscedastic consistent ridge estimator that efficiently controls the adverse effect of heteroscedastic error term. Our suggestion is based on a novel idea of estimating the error variance using the heteroscedasticity consistent covariance matrix estimator. The suggested approach works well in terms of heteroscedastic as well as homoscedastic scenarios too. We have evaluated the performance of suggested modified estimators with the help of simulations and have illustrated it by applications to real-life datasets. This improvement will help to efficiently handle the estimation problem in these two challenging scenarios. [ABSTRACT FROM AUTHOR]

The framework of heteroscedastic extremes developed by Einmahl et al. (2016) has become an important research area due to its contribution to trend detection. While a previous work of Mefleh et al. (2020) studies some parametric trend models, this article constitutes a small extension to another practical case: the simple change point model where the change point is assumed to be known in time. We first study the model theoretically, estimate the parameter by maximum likelihood method and show its consistency and asymptotic normality. We then associate the proposed model with the discrete log-linear trend model previously developed in Mefleh et al. (2020). We finally verify the results by a simulation and apply the model to real data. [ABSTRACT FROM AUTHOR]

In this paper, the one-sided hypothesis testing and interval estimation problems for the fixed effect and variance component functions are considered in the skew-normal unbalanced heteroscedastic one-way classification random effects model. Firstly, the Bootstrap approach is used to establish test statistic for fixed effect. Secondly, the test statistics and confidence intervals for variance component functions are constructed by Bootstrap approach and generalized approach, and their theoretical properties are discussed. The Monte Carlo simulation results indicate that the Bootstrap approach performs better than the generalized approach in most cases. Finally, the above approaches are illustrated with two real examples of the annual average concentrations of fine particulate matter and nitrogen dioxide. [ABSTRACT FROM AUTHOR]

We propose a family of CUSUM-based statistics to detect the presence of changepoints in the deterministic part of the autoregressive parameter in a Random Coefficient Autoregressive (RCA) sequence. Our tests can be applied irrespective of whether the sequence is stationary or not, and no prior knowledge of stationarity or lack thereof is required. Similarly, our tests can be applied even when the error term and the stochastic part of the autoregressive coefficient are non iid, covering the cases of conditional volatility and shifts in the variance, again without requiring any prior knowledge as to the presence or type thereof. In order to ensure the ability to detect breaks at sample endpoints, we propose weighted CUSUM statistics, deriving the asymptotics for virtually all possible weighing schemes, including the standardized CUSUM process (for which we derive a Darling-Erdős theorem) and even heavier weights (so-called Rényi statistics). Simulations show that our procedures work very well in finite samples. We complement our theory with an application to several financial time series. [ABSTRACT FROM AUTHOR]

This document is a comment on a previous article about the estimation of prediction error in linear regression models. It provides a different perspective and focuses on linear models, including nonparametric regression fitting methods. The comment discusses the standard result for the expected value of a quadratic form and examines prediction errors in a standard linear model. It also discusses the use of prediction ellipsoids and significance tests in linear models, emphasizing the importance of estimating the covariance matrix and comparing it to the mean squared error to determine the reasonableness of the models. The document also discusses the issue of overfitting in statistical modeling and its impact on predictions and variance estimates. It explains that overfitting occurs when a model is too complex and fits the current data too closely, resulting in poor predictions for new data. The document also discusses the estimation of heteroscedasticity in statistical models and the challenges of estimating parameters with limited observations. It concludes by mentioning that the estimation of squared residuals can be used as an unbiased estimator of the variance in the homoscedastic case, but not in the heteroscedastic case. Lastly, the document discusses the estimation of low leverage points in a linear model and the estimation of v using least squares. The author concludes that the estimate is reasonable if one accepts the linear model for the variances. [Extracted from the article]

Bootstrapping tests U ∗ are implemented for the tests U by Schmidt [Detecting changes in the trend function of heteroscedastic time series; 2021. Preprint: arXiv:2108.09206 [math.ST]] for mean break and Schmidt et al. [An asymptotic test for constancy of the variance under short-range dependence. Ann Stat. 2021;49:3460–3481.] for variance break based on U-statistics. The tests U have good powers against epidemic breaks that are common in practice. The test U for variance break is proved to have the nice property of consistency against a general class of alternatives. However, the tests U have non-ignorable finite sample size distortion under serial correlation and/or conditional heteroscedasticity. Our implementation U ∗ based on autoregressive residual bootstrapping and moving block bootstrapping are shown to remedy the size distortion problems of U for mean break and for variance break, respectively, in a Monte-Carlo experiment. The experiment also demonstrates the power advantages of bootstrapping tests over the original tests and other standard break tests against epidemic breaks, which, however, are accompanied by disadvantages against simple single breaks. The proposed bootstrapping tests are well illustrated by break analyses of means and variances of the log-return and realized the volatility of the US S&P 500. [ABSTRACT FROM AUTHOR]

In this article, a quasi-maximum of likelihood approach, with minimal assumptions and computational performances, is proposed to estimate the coefficients of the two dimensionally indexed Generalized Autoregressive model. First, sufficient conditions of the existence of a strict stationary solution are given. In a second step, we propose consistent estimators of the parameter vector of interest, even if we are in doubt about the distribution, by minimizing the Kullback–Leiber divergence between the true distribution and a misspecified parametric family of hypothesized distribution. Results of numerical simulations are presented at the end. [ABSTRACT FROM AUTHOR]

In this article, we test for the effects of high-dimensional covariates on the response. In many applications, different components of covariates usually exhibit various levels of variation, which is ubiquitous in high-dimensional data. To simultaneously accommodate such heteroscedasticity and high dimensionality, we propose a novel test based on an aggregation of the marginal cumulative covariances, requiring no prior information on the specific form of regression models. Our proposed test statistic is scale-invariance, tuning-free and convenient to implement. The asymptotic normality of the proposed statistic is established under the null hypothesis. We further study the asymptotic relative efficiency of our proposed test with respect to the state-of-art universal tests in two different settings: one is designed for high-dimensional linear model and the other is introduced in a completely model-free setting. A remarkable finding reveals that, thanks to the scale-invariance property, even under the high-dimensional linear models, our proposed test is asymptotically much more powerful than existing competitors for the covariates with heterogeneous variances while maintaining high efficiency for the homoscedastic ones. for this article are available online. [ABSTRACT FROM AUTHOR]

Understanding how microbes interact with each other is key to revealing the underlying role that microorganisms play in the host or environment and to identifying microorganisms as an agent that can potentially alter the host or environment. For example, understanding how the microbial interactions associate with parasitic infection can help resolve potential drug or diagnostic test for parasitic infection. To unravel the microbial interactions, existing tools often rely on graphical models to infer the conditional dependence of microbial abundances to represent their interactions. However, current methods do not simultaneously account for the discreteness, compositionality, and heterogeneity inherent to microbiome data. Thus, we build a new approach called "compositional graphical lasso" upon existing tools by incorporating the above characteristics into the graphical model explicitly. We illustrate the advantage of compositional graphical lasso over current methods under a variety of simulation scenarios and on a benchmark study, the Tara Oceans Project. Moreover, we present our results from the analysis of a dataset from the Zebrafish Parasite Infection Study, which aims to gain insight into how the gut microbiome and parasite burden covary during infection, thus, uncovering novel putative methods of disrupting parasite success. Our approach identifies changes in interaction degree between infected and uninfected individuals for three taxa, Photobacterium, Gemmobacter, and Paucibacter, which are inversely predicted by other methods. Further investigation of these method-specific taxa interaction changes reveals their biological plausibility. In particular, we speculate on the potential pathobiotic roles of Photobacterium and Gemmobacter in the zebrafish gut, and the potential probiotic role of Paucibacter. Collectively, our analyses demonstrate that compositional graphical lasso provides a powerful means of accurately resolving interactions between microbiota and can thus drive novel biological discovery. for this article are available online. [ABSTRACT FROM AUTHOR]