Search

A computationally simple bias correction for linear dynamic panel data models is proposed and its asymptotic properties are studied when the number of time periods is fixed or tends to infinity with the number of panel units. The approach can accommodate both fixed-effects and random-effects assumptions, heteroskedastic errors, as well as higher-order autoregressive models. Panel-corrected standard errors are proposed that allow for robust inference in dynamic models with cross-sectionally correlated errors. Monte Carlo experiments suggest that under the assumption of strictly exogenous regressors the bias-corrected method of moment estimator outperforms popular GMM estimators in terms of efficiency and correctly sized tests.

Asymptotic properties of classical kernel estimators for the spectral density are studied in the locally stationary framework. In particular, it is shown that for a locally stationary process standard spectral density estimators consistently estimate the time-averaged spectral density. This result is complemented by some illustrative examples and applications including HAC-inference in the multiple linear regression model, a simple visual tool for the detection of unconditional heteroskedasticity and a test for covariance stationarity.

We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the now-standard conformal prediction for uncertainty quantification, with novel theoretical insights and computational advantages. The data-adaptive prediction band is universally applicable with minimal distributional assumptions, has strong non-asymptotic coverage properties, and is easy to implement using standard convex programs. Our approach can be viewed as a novel variance interpolation with confidence and further leverages techniques from semi-definite programming and sum-of-squares optimization. Theoretical and numerical performances for the proposed approach for uncertainty quantification are analyzed., 21 pages, 4 figures

Statistical applications often involve a comparison of coefficients across two different nested linear regression specifications. However, these comparisons are rarely accompanied by a hypothesis test for the coefficients being equal. Standard specification tests from econometrics, while easy to apply, are not useful in this case. Generalized versions of these tests can be seen as essentially applying the delta method to the omitted-variable-bias formula, but have a tendency to over-reject, especially in small samples when errors are heteroskedastic. Resampling procedures can be helpful in this case, with approaches associated with the jackknife performing particularly well in conducting this test.

The problem of fitting two concentric objects (circles and ellipses) to noisy data plays a vital role in many fields. In this paper, statistical methodologies are deployed by additionally assuming that the angular differences between successively measured data points are known, which is known as Berman’s model. The heteroscedasticity between covariates is also assumed here, and hence, several estimators for the problem of fitting concentric circles and ellipses are developed and their statistical properties are established. Unlike concentric circles, the problem of fitting concentric ellipses turns out to be nonlinear even with Berman’s assumption, and as such, iterative algorithms are implemented. Extensive numerical experiments were conducted to validate our results.

This article constructs individual-specific density forecasts for a panel of firms or households using a dynamic linear model with common and heterogeneous coefficients as well as cross-sectional heteroscedasticity. The panel considered in this article features a large cross-sectional dimension N but short time series T. Due to the short T, traditional methods have difficulty in disentangling the heterogeneous parameters from the shocks, which contaminates the estimates of the heterogeneous parameters. To tackle this problem, I assume that there is an underlying distribution of heterogeneous parameters, model this distribution nonparametrically allowing for correlation between heterogeneous parameters and initial conditions as well as individual-specific regressors, and then estimate this distribution by combining information from the whole panel. Theoretically, I prove that in cross-sectional homoscedastic cases, both the estimated common parameters and the estimated distribution of the heterogeneous parameters achieve posterior consistency, and that the density forecasts asymptotically converge to the oracle forecast. Methodologically, I develop a simulation-based posterior sampling algorithm specifically addressing the nonparametric density estimation of unobserved heterogeneous parameters. Monte Carlo simulations and an empirical application to young firm dynamics demonstrate improvements in density forecasts relative to alternative approaches.

Strong consistency and asymptotic normality of a Gaussian quasi-maximum likelihood estimator for the parameters of a causal, invertible, and identifiable vector autoregressive-moving average (VARMA) model are established in an indirect way. The proof is based on similar results for a much wider class of VARMA models with time-dependent coefficients, hence in the context of non-stationary and heteroscedastic time series. For that reason, the proof avoids spectral analysis arguments and does not make use of ergodicity. The results presented are also applicable to ARMA models.

Using daily mutual fund returns to estimate market timing, some econometric issues, including heteroscedasticity, correlated errors, and heavy tails, make the traditional least squares estimate in ...

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 imp...

There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive models with heavy tailed, weakly dependent innovations with virtually no assumption on the conditional heteroskedasticity. In contrast to current literature, our innovation process satisfy an $L^1$ mixingale type condition on the centered conditional covariance matrices. This condition covers $L^1$-NED sequences and strong ($\alpha$-) mixing sequences as particular examples.

In this paper, we introduce a class of periodic negative binomial integer-valued generalized autoregressive conditional heteroskedastic model. The basic probabilistic and statistical properties of ...

We consider a model whereby a given response variable Y following a transformation $${{\mathcal {Y}}}:=\mathcal {T}(Y)$$ , satisfies some classical regression equation. In this transformation model the form of the transformation is specified analytically but incorporates an unknown transformation parameter. We develop testing procedures for the null hypothesis of homoskedasticity for versions of this model where the regression function is considered either known or unknown. The test statistics are formulated on the basis of Fourier-type conditional contrasts of a variance computed under the null hypothesis against the same quantity computed under alternatives. The limit null distribution of the test statistic is studied, as well as the behaviour of the test criterion under alternatives. Since the limit null distribution is complicated, a bootstrap version is suggested in order to actually carry out the test procedures. Monte Carlo results are included that illustrate the finite-sample properties of the new method. The applicability of the new tests on real data is also illustrated.

The problem of inference in a standard linear regression model with heteroskedastic errors is investigated. A GLS estimator which is based on a nonparametric kernel estimator is proposed for the volatility process. It is shown that the resulting feasible GLS estimator is T -consistent for a wide range of deterministic and stochastic processes for the time-varying volatility. Moreover, the kernel-GLS estimator is asymptotically more efficient than OLS and hence inference based on its asymptotic distribution is sharper. A Monte Carlo exercise is designed to study the finite sample properties of the proposed estimator and it is shown that tests based on it are correctly-sized for a variety of DGPs. As expected, it is found that in some cases, testing based on OLS is invalid. Crucially, even in cases when tests based on OLS or OLS with heteroskedasticity-consistent (HC) standard errors are correctly-sized, it is found that inference based on the proposed GLS estimator is more powerful even for relatively small sample sizes.

High throughput sequencing (HTS)-based technology enables identifying and quantifying non-culturable microbial organisms in all environments. Microbial sequences have enhanced our understanding of the human microbiome, the soil and plant environment, and the marine environment. All molecular microbial data pose statistical challenges due to contamination sequences from reagents, batch effects, unequal sampling, and undetected taxa. Technical biases and heteroscedasticity have the strongest effects, but different strains across subjects and environments also make direct differential abundance testing unwieldy. We provide an introduction to a few statistical tools that can overcome some of these difficulties and demonstrate those tools on an example. We show how standard statistical methods, such as simple hierarchical mixture and topic models, can facilitate inferences on latent microbial communities. We also review some nonparametric Bayesian approaches that combine visualization and uncertainty quantification. The intersection of molecular microbial biology and statistics is an exciting new venue. Finally, we list some of the important open problems that would benefit from more careful statistical method development.

Generalized estimating equations [Image: see text] are widely used to analyze longitudinal data; however, they are not appropriate for heteroscedastic data, because they only estimate regressor effects on the mean response – and therefore do not account for data heterogeneity. Here, we combine the [Image: see text] with the asymmetric least squares (expectile) regression to derive a new class of estimators, which we call generalized expectile estimating equations [Image: see text] . The [Image: see text] model estimates regressor effects on the expectiles of the response distribution, which provides a detailed view of regressor effects on the entire response distribution. In addition to capturing data heteroscedasticity, the GEEE extends the various working correlation structures to account for within-subject dependence. We derive the asymptotic properties of the [Image: see text] estimators and propose a robust estimator of its covariance matrix for inference (see our R package, github.com/AmBarry/expectgee). Our simulations show that the GEEE estimator is non-biased and efficient, and our real data analysis shows it captures heteroscedasticity.

AR ve ARMA tahminleri, eldeki bir seri için temel bir matematiksel ifadeyi belirlemek açısından iyi bilinen araçlar olmaya devam etmektedir. Matematiksel bir denklem elde edildiğinde, girdi ve çıktı arasında bir transfer fonksiyonu türetmek mümkündür. Bu transfer fonksiyonunun kutupları birim çemberin üzerinde veya dışında yer alıyorsa, üretilen seri durağan olmayacaktır. Önemli sayıda numunenin üretildiği böyle bir seri, bir simülasyon etkinliği için tamsayı taşmalarına neden olacaktır. Çalışma için, Hatalar Arası Ortlama Zaman (HAOZ) gözlem amaçlı doğrulama serisi, bir Endüstriyel Gömülü PC İletişimi Sınama yatağından alınmıştır. Bunlar zaman ve sıklık açısından AR ve ARMA tarafından tahmin edilenlerle karşılaştırılır. AR tahmini, durağan özelliği koruyan 57 derecelik bir polinom durumunda, orijinal gözlemle daha iyi bir eşleşmeye sahiptir., The AR and ARMA estimations remain well-known tools for determining an underlying mathematical expression for a series at hand. Once a mathematical equation is obtained, it is possible to derive a transfer function between the input and output. If the poles of this transfer function reside on or outside the unit circle, the series generated would not be stationary. Such a series with a significant number of samples generated would cause integer overflows for a simulation activity. For the study, the MTBF observation purposed validation series is considered from an Industrial Embedded PC Communications Test-Bed. These are compared on time and frequency to AR and ARMA estimated ones. The AR estimation possesses a better match to the original, with a 57-degree polynomial maintaining the stationary property.

In many settings, data acquisition generates outliers that can obscure inference. Therefore, practitioners often either identify and remove outliers or accommodate outliers using robust models. However, identifying and removing outliers is often an ad hoc process that affects inference, and robust methods are often too simple for some applications. In our motivating application, scientists drill snow cores and measure snow density to infer densification rates that aid in estimating snow water accumulation rates and glacier mass balances. Advanced measurement techniques can measure density at high resolution over depth but are sensitive to core imperfections, making them prone to outliers. Outlier accommodation is challenging in this setting because the distribution of outliers evolves over depth and the data demonstrate natural heteroscedasticity. To address these challenges, we present a two-component mixture model using a physically motivated snow density model and an outlier model, both of which evolve over depth. The physical component of the mixture model has a mean function with normally distributed depth-dependent heteroscedastic errors. The outlier component is specified using a semiparametric prior density process constructed through a normalized process convolution of log-normal random variables. We demonstrate that this model outperforms alternatives and can be used for various inferential tasks.

We propose a new test to validate the assumption of homoscedasticity in a functional linear model. We consider a minimum distance measure of heteroscedasticity in functional data, which is zero in the case where the variance is constant and positive otherwise. We derive an explicit form of the measure, propose an estimator for the quantity, and show that an appropriately standardized version of the estimator is asymptotically normally distributed under both the null (homoscedasticity) and alternative hypotheses. We extend this result for residuals from functional linear models and develop a bootstrap diagnostic test for the presence of heteroscedasticity under the postulated model. Moreover, our approach also allows testing for “relevant” deviations from the homoscedastic variance structure and constructing confidence intervals for the proposed measure. We investigate the performance of our method using extensive numerical simulations and a data example.

There is a vast amount of work on high-dimensional regression. The common starting point for the existing theoretical work is to assume the data generating model is a homoscedastic linear regressio...

This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors. An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix. The admissibility of designs is also considered and a sufficient condition to simplify the design problem is obtained. The results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.

This article proposes a novel multivariate generalized autoregressive conditionally heteroscedastic (GARCH) model that incorporates the modified Cholesky decomposition for a covariance matrix in or...

Commodity price stationarity grants good predictability and effective policy intervention. The analysis at the quantiles shows that prices are stationary at the lower but not at the higher quantiles. The non-stationarity of commodity prices is often related to the behavior of the US exchange rate series. Quantile regression estimates show changing coefficients across quantiles. This signals the presence of heteroscedasticity in the series. Stationarity holds throughout once the series are corrected for heteroscedasticity, exchange rate included. This finding weakens the claim that exchange rates cause persistence in commodity prices. The price-exchange rate correlation mirrors their common heteroscedasticity. The correlation declines in the cleaned/homoscedastic series.

Interrupted time series (ITS) design is commonly used to evaluate the impact of interventions in healthcare settings. Segmented regression (SR) is the most commonly used statistical method and has been shown to be useful in practical applications involving ITS designs. Nevertheless, SR is prone to aggregation bias, which leads to imprecision and loss of power to detect clinically meaningful differences. The objective of this article is to present a weighted SR method, where variability across patients within the healthcare facility and across time points is incorporated through weights. We present the methodological framework, provide optimal weights associated with data at each time point and discuss relevant statistical inference. We conduct extensive simulations to evaluate performance of our method and provide comparative analysis with the traditional SR using established performance criteria such as bias, mean square error and statistical power. Illustrations using real data is also provided. In most simulation scenarios considered, the weighted SR method produced estimators that are uniformly more precise and relatively less biased compared to the traditional SR. The weighted approach also associated with higher statistical power in the scenarios considered. The performance difference is much larger for data with high variability across patients within healthcare facilities. The weighted method proposed here allows us to account for the heterogeneity in the patient population, leading to increased accuracy and power across all scenarios. We recommend researchers to carefully design their studies and determine their sample size by incorporating heterogeneity in the patient population.

In stratified sampling, ever since Dalenius [1] undertook the problem of optimum stratification, the research in the area has been progressing in various perspectives and dimensions till date. Amidst the multifaceted developments in the trend of the research, consideration of the topic by taking into account various aspects such as different sample selection methods and allocations, study variable based stratification, auxiliary variable based stratification, superpopulation models, extension to two study variables for a single auxiliary variable, extension to two stratification variables for a single study variable etc., are a few noteworthy ones. However, with regard to considering optimum stratification of heteroscedastic populations, as live populations are generally heteroscedastic, it was Gupt and Ahamed [2,3] who considered the problem for a few allocations under a heteroscedastic regression superpopulation (HRS) model. As a sequel to the work of the authors, in this paper, the problem of optimum stratification for an objective variable y based on a concomitant variable x under the HRS model is considered for an allocation proposed by Gupt [4,5] and termed as Generalised Auxiliary Variable Optimum Allocation (GAVOA). Methods of stratification in the form of equations and approximate solutions to the equations which stratify populations at optimum strata boundaries (OSB) and approximately optimum strata boundaries (AOSB) respectively are obtained. Mathematical analysis is used in minimizing sampling variance of the estimator of population mean and deriving all the proposed methods of stratification. The proposed equations divide heteroscedastic populations, symmetrical or moderately skewed or highly skewed, at OSB, but, the equations are implicit in nature and not easy in solving. Therefore, a few methods of finding AOSB are deduced from the equations through analytically justified steps of approximation. The methods may provide practically feasible solutions in survey planning in stratifying heteroscedastic population of any level of heteroscedasticity and the work may contribute, to some extent, theoretically in the research area. The methods are empirically examined in a few generated heteroscedastic data of varied shapes with some assumed levels of heteroscedasticity and found to perform with high efficiency. The proposed methods of stratification are restricted to the particular allocation used.

In this paper, we present new two-stage multiple comparison procedures with the average for location parameters of two-parameter exponential distributions under heteroscedasticity by modifying the ...

We propose a piecewise linear quantile trend model to analyse the trajectory of the COVID-19 daily new cases (i.e. the infection curve) simultaneously across multiple quantiles. The model is intuitive, interpretable and naturally captures the phase transitions of the epidemic growth rate via change-points. Unlike the mean trend model and least squares estimation, our quantile-based approach is robust to outliers, captures heteroscedasticity (commonly exhibited by COVID-19 infection curves) and automatically delivers both point and interval forecasts with minimal assumptions. Building on a self-normalized (SN) test statistic, this paper proposes a novel segmentation algorithm for multiple change-point estimation. Theoretical guarantees such as segmentation consistency are established under mild and verifiable assumptions. Using the proposed method, we analyse the COVID-19 infection curves in 35 major countries and discover patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. A simple change-adaptive two-stage forecasting scheme is further designed to generate short-term prediction of COVID-19 cumulative new cases and is shown to deliver accurate forecast valuable to public health decision-making.

In this paper, we present a modified one-stage multiple comparison procedure for exponential location parameters with the control under heteroscedasticity including one-sided and two-sided confiden...

The two one-sided tests (TOST) procedure is the common method for assessing bioequivalence between two different drugs or formulations of the same drug. Several solutions to Behrens-Fisher problem ...

The Least-Squares Monte Carlo (LSMC) method has gained popularity in recent years due to its ability to handle multi-dimensional stochastic control problems, including problems with state variables affected by control. However, when applied to the stochastic control problems in the multi-period expected utility models, such as finding optimal decisions in life-cycle expected utility models, the regression fit tends to contain errors which accumulate over time and typically blow up the numerical solution. In this paper we propose to transform the value function of the problems to improve the regression fit, and then using either the smearing estimate or smearing estimate with controlled heteroskedasticity to avoid the re-transformation bias in the estimates of the conditional expectations calculated in the LSMC algorithm. We also present and utilise recent improvements in the LSMC algorithms such as control randomisation with policy iteration to avoid accumulation of regression errors over time. Presented numerical examples demonstrate that transformation method leads to an accurate solution. In addition, in the forward simulation stage of the control randomisation algorithm, we propose a re-sampling of the state and control variables in their full domain at each time t and then simulating corresponding state variable at $$t+1$$ , to improve the exploration of the state space that also appears to be critical to obtain a stable and accurate solution for the expected utility models.

An important and widely used class of semiparametric models is formed by the varying-coefficient models. Although the varying coefficients are traditionally assumed to be smooth functions, the varying-coefficient model is considered here with the coefficient functions containing a finite set of discontinuities. Contrary to the existing nonparametric and varying-coefficient estimation of piecewise smooth functions, the varying-coefficient models are considered here under dependence and are applicable in time series with heteroskedastic and serially correlated errors. Additionally, the conditional error variance is allowed to exhibit discontinuities at a finite set of points too. The (uniform) consistency and asymptotic normality of the proposed estimators are established and the finite-sample performance is tested via a simulation study and in a real-data example.

Minimax robust designs for regression models with heteroscedastic errors are studied and constructed. These designs are robust against possible misspecification of the error variance in the model. We propose a flexible assumption for the error variance and use a minimax approach to define robust designs. As usual it is hard to find robust designs analytically, since the associated design problem is not a convex optimization problem. However, we can show that the objective function of the minimax robust design problem is a difference of two convex functions. An effective algorithm is developed to compute minimax robust designs under the least squares estimator and generalized least squares estimator. The algorithm can be applied to construct minimax robust designs for any linear or nonlinear regression model with heteroscedastic errors. In addition, several theoretical results are obtained for the minimax robust designs.

We propose a GARCH model for uncorrelated, integer‐valued time series that exhibit conditional heteroskedasticity. Conditioned on past information, these observations have a two‐sided Poisson distribution with time‐varying variance. Positive and negative observations can have an asymmetric impact on conditional variance. We give conditions under which the proposed integer‐valued GARCH process is stationary, ergodic, and has finite moments. We consider maximum likelihood estimation for model parameters, and we give the limiting distribution for these estimators when the true parameter vector is in the interior of its parameter space, and when some GARCH coefficients are zero.

Adjusting for baseline values and covariates is a recurrent statistical problem in medical science. In particular, variance heteroscedasticity is non-negligible in experimental designs and ignoring it might result in false conclusions. Approximate inference methods are developed to test null hypotheses formulated in terms of adjusted treatment effects and regression parameters in general analysis of covariance designs with arbitrary numbers of factors. Variance homoscedasticity is not assumed. The distributions of the test statistics are approximated using Box-type approximation methods. Extensive simulation studies show that the procedures are particularly suitable when sample sizes are rather small. A real data set illustrates the application of the methods.

This article extends spatial autoregressive model with spatial autoregressive disturbances (SARAR(1,1)) which is the most popular spatial econometric model to the case of an arbitrary finite number...

We propose new break tests for parameters such as mean, variance, quantile and others of panel data sets, in a general setup based on the self-normalization method. The self-normalization tests show much better size than existing tests, resolving their over-size problem for panels with serial dependence, cross-sectional dependence, conditional heteroscedasticity and/or N relative larger than T, which is demonstrated theoretically by a nuisance parameter free limiting null distribution and experimentally by very stable finite sample sizes. The proposed test is also implemented much more easily than the existing tests in that the proposed test needs no bandwidth selection for the long-run variance estimation and is computed very simply. Applications of the self-normalization test to the financial stock return and realized volatility indicate more toward absence of breaks of mean and/or variance than the existing tests which neglect cross-sectional correlation and other features apparent in the data sets.

In proxy vector autoregressive models, the structural shocks of interest are identified by an instrument. Although heteroscedasticity is occasionally allowed for in inference, it is typically taken...

ANOVA under normally distributed response and heteroscedastic variances is commonly encountered in biological, behavioral, educational and agricultural sciences where the commonly used F-test is not valid. Many alternatives suggested in the literature exhibit unsatisfactory performance with respect to the type-I errors notably under a large number of small size groups. This has a direct bearing on their power performance. Anticipating that a major cause may be the existence of a large number of unknown unequal group variances as nuisance parameters, the present work attempts to provide a uniformly implementable simple solution that addresses this problem through the use of likelihood integration with respect to the nuisance parameters. The second-order accurate asymptotic $$\chi ^2$$ distribution of the test is established. Simple ad hoc corrective adjustments suggested for enhancing the small sample distributional performance make the test usable even for small group sizes. Simulation studies demonstrate that the test exhibits uniformly well-concentrated sizes at the desired level and the best power, particularly under very small size groups, highly scattered group variances and/or a large number of groups under one-way and two-way ANOVA where precisely a better option is needed. Being closely competent to other peers in all other cases, it offers an universally implementable and trustworthy option in this scenario. The method is straightway extendable to multi-factor setup and has direct connection to ANOVA under log-normally distributed data. Results are illustrated with real data.

Models for heteroskedastic data are relevant in a wide variety of applications ranging from financial time series to environmental statistics. However, the topic of modeling the variance function conditionally has not seen near as much attention as modeling the mean. Volatility models have been used in specific applications, but these models can be difficult to fit in a Bayesian setting due to posterior distributions that are challenging to sample from efficiently. In this work, we introduce a general model for heteroskedastic data. This approach models the conditional variance in a mixed model approach as a function of any desired covariates or random effects. We rely on new distribution theory in order to construct priors that yield fully conjugate full conditional distributions. Thus, our approach can easily be fit via Gibbs sampling. Furthermore, we extend the model to a deep learning approach that can provide highly accurate estimates for time dependent data. We also provide an extension for heavy-tailed data. We illustrate our methodology via three applications. The first application utilizes a high dimensional soil dataset with inherent spatial dependence. The second application involves modeling of asset volatility. The third application focuses on clinical trial data for creatinine.

Multivariate data is collected in many fields, such as chemometrics, econometrics, financial engineering and genetics. In multivariate data, heteroscedasticity and collinearity occur frequently. And selecting material predictors is also a key issue when analyzing multivariate data. To accomplish these tasks, multivariate linear regression model is often constructed. We thus propose row-sparse elastic-net regularized multivariate Huber regression model in this paper. For this new model, we proof its grouping effect property and the property of resisting sample outliers. Based on the KKT condition, an accelerated proximal sub-gradient algorithm is designed to solve the proposed model and its convergency is also established. To demonstrate the accuracy and efficiency, simulation and real data experiments are carried out. The numerical results show that the new model can deal with heteroscedasticity and collinearity well.

This study focuses on examining the power of bootstrapped and exact tests to detect variance heterogeneity in linear models via Monte Carlo. Three independent MC schemes were set up corresponding t...

When estimating the average causal effect in observational studies, researchers have to tackle both self-selection of treatment and outcome modeling. This is difficult because the parametric form of the outcome model is often unknown and there exists a large number of covariates. In this work, we present a semiparametric strategy for estimating the average causal effect by regressing on the propensity score. Furthermore, we show that regression error terms usually depend on the propensity score as well, which could cause heteroscedastic variances, and thus construct a refined estimator to improve the estimation efficiency. Both estimators are shown to be consistent and asymptotically normally distributed, with the latter one having a smaller asymptotic variance. The simulation studies indicate that our methods compare favorably with many competing estimators. Our methods are easy to implement and avoid hazardous impact due to extreme weights as often seen in weighting estimators. They can also be extended to handle subgroup effects with known structure. We apply the proposed methods to data from the Ohio Medicaid Assessment Survey 2012, estimating the effect of having health insurance on self-reported health status for a population with subsidized insurance plan choices under the Affordable Care Act.

Tests for variance or scale effects due to covariates are used in many areas and recently, in genomic and genetic association studies. We study score tests based on location-scale models with arbitrary error distributions that allow incorporation of additional adjustment covariates. Tests based on Gaussian and Laplacian double generalized linear models are examined in some detail. Numerical properties of the tests under Gaussian and other error distributions are examined. Our results show that the use of model-based asymptotic distributions with score tests for scale effects does not control type 1 error well in many settings of practical relevance. We consider simple statistics based on permutation distribution approximations, which correspond to well-known statistics derived by another approach. They are shown to give good type 1 error control under different error distributions and under covariate distribution imbalance. The methods are illustrated through a differential gene expression analysis involving breast cancer tumor samples.

An adaptive-weighted estimation procedure for parametric and nonparametric coefficients in semi-varying coefficient models with heteroscedastic errors is considered in this paper. Firstly, we prese...

This work aims to deduce estimators for the unknown parameters of fixed effects and covariance matrix structure in heteroscedastic additive design. In order to do that, the design will be projected onto the orthogonal complement of the subspace spanned by columns of design matrix for the fixed effects, and the Kronecker product will be used to produced unbiased estimators for the parameters of covariance matrix, and then such estimators used to produce an estimator for the fixed effect vector. Moreover, the coefficient of determination for both fixed effects and covariance structure will be derived. A simulation study will be conducted, and a numerical example will be explored.

The issue of heteroscedasticity and its adverse impact on the estimation of a linear regression model has been extensively discussed in the available literature. Some adaptive estimators have also ...

In this article, we focus on the efficient estimation in single-index models with heteroscedastic errors. We first develop a nonparametric estimator of the variance function based on a fully nonpar...

The multivariate finite normal mixture model is one of the most commonly used tools to analyze a heterogeneous data. When using the multivariate finite normal mixture model, one is usually interested in knowing whether a homoscedastic mixture model can be used to simplify the model. The likelihood ratio test (LRT) is the most popular statistic tool to choose between two nested models. Under the null model of a homoscedastic multivariate normal mixture, the asymptotic χ 2 distribution is commonly used to approximate the null distribution of the LRT statistic. However, it is demonstrated using numerical studies that the χ 2 distribution approximation is not satisfactory and fails to control the nominal type I error unless the sample size is larger than 2000, the mixture components are well-separated, and the singular solutions are avoided. A parametric bootstrap method is further proposed to approximate the distribution of the LRT statistic and its effectiveness is evaluated through extensive numerical studies.

The properties of the heteroscedasticity non-consistent variances and heteroscedasticity consistent variances are reviewed. Unlike the related existing results, the following cases are discussed separately: (i) the cases where the explanatory variables are strictly exogenous; and (ii) the cases where the explanatory variables may or may not be strictly exogenous. The latter cases allow weakly dependent explanatory variables such as those generating from an autoregressive process. New results on the original robust variance (denoted by H C 0 ) and its variants (denoted by H C 1 , H C 2 , H C 3 , H C 4 and H C j ) are derived. In particular, the followings are shown: (i) the ordering of the original robust variance and its variants; (ii) the asymptotic equivalence among different variants of robust variance; and (iii) under quadratic form of heteroscedasticity (with mesokurtic/leptokurtic normalized error) or GARCH(1,1)-error, non-robust variance rejects more often than robust variance. Simulation studies suggest H C 4 by and large does not over-rejects or mildly under-rejects.