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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]

Scaling is common in empirical accounting research. It is often done to mitigate heteroscedasticity or the influence of firm size on parameter estimates. However, Barth and Clinch conclude that common diagnostic tools are ineffective in detecting various scale effects. Using analytic results and Monte Carlo simulations, we show that common forms of scaling, when misapplied, induce substantial spurious correlation via biased parameter estimates. Researchers, when uncertain about the exact functional form of scale effect, are typically better off dealing with both heteroscedasticity and the influence of larger firms using techniques other than scaling. [ABSTRACT FROM AUTHOR]

Time-resolved microscopy is a widely used approach for imaging and quantifying charge and energy transport in functional materials. While it is generally recognized that resolving small diffusion lengths is limited by measurement noise, the impacts of noise have not been systematically assessed or quantified. This article reports modeling efforts to elucidate the impact of noise on optical probes of transport. Excited state population distributions, modeled as Gaussians with additive white noise typical of experimental conditions, are subject to decay and diffusive evolution. Using a conventional composite least-squares fitting algorithm, the resulting diffusion constant estimates are compared with the model input parameter. The results show that heteroscedasticity (i.e., time-varying noise levels), insufficient spatial and/or temporal resolution, and small diffusion lengths relative to the magnitude of noise lead to a surprising degree of imprecision under moderate experimental parameters. Moreover, the compounding influence of low initial contrast and small diffusion length leads to systematic overestimation of diffusion coefficients. Each of these issues is quantitatively analyzed herein, and experimental approaches to mitigate them are proposed. General guidelines for experimentalists to rapidly assess measurement precision are provided, as is an open-source tool for customizable evaluation of noise effects on time-resolved microscopy transport measurements. [ABSTRACT FROM AUTHOR]

ABSTRACT Independent censoring is usually assumed in survival data analysis. However, dependent censoring, where the survival time is dependent on the censoring time, is often seen in real data applications. In this project, we model the vector of survival time and censoring time marginally through semiparametric heteroscedastic accelerated failure time models and model their association by the vector of errors in the model. We show that this semiparametric model is identified, and the generalized estimating equation approach is extended to estimate the parameters in this model. It is shown that the estimators of the model parameters are consistent and asymptotically normal. Simulation studies are conducted to compare it with the estimation method under a parametric model. A real dataset from a prostate cancer study is used for illustration of the new proposed method. [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]

This study is directed at gauging the equity price risk of the Indian commercial banks for the period 2003–2020. Parametric value-at-risk (VaR) is employed to estimate the downside risk. Further, the univariate exponential generalized auto regressive conditional heteroskedasticity (EGARCH) model is also used to find out the existence of stylised aspects of volatility. The outcomes point towards the existence of volatility clustering, persistence and asymmetry, but differ from bank to bank. Furthermore, the parametric VaR model that assumes normal distribution and student's t -distribution is not found to be an accurate model for all the banks. Tail risk is also found to be significant, and thus, justifies the Basel Committee's decision to shift towards an expected shortfall. However, these conventional VaR models should be supplemented by internal models, taking into consideration, bank-specific characteristics. JEL: G01, G15, I15, G17, G28 [ABSTRACT FROM AUTHOR]

In this article, we consider an empirical likelihood with vector observations that are martingale differences and prove a Wilks' type theorem under a conditional Lindeberg condition. We then generalize this result to approximate martingale differences. As applications of the first result we discuss the construction of confidence regions for various time series models, including linear and nonlinear autoregressive models, an ARCH(1) model, and nonlinear autoregressive models with heteroskedasticity. The second result is used to derive a Wilks' type theorem for a blockwise empirical likelihood for Markov chains. [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 complex nature of microbiome data has made the differential abundance analysis challenging. Microbiome abundance counts are often skewed to the right and heteroscedastic (also known as overdispersion), potentially leading to incorrect inferences if not properly addressed. In this paper, we propose a simple yet effective framework to tackle the challenges by integrating Poisson (log-linear) regression with standard error estimation through the Bootstrap method and Sandwich robust estimation. Such standard error estimates are accurate and yield satisfactory inference even if the distributional assumption or the variance structure is incorrect. Our approach is validated through extensive simulation studies, demonstrating its effectiveness in addressing overdispersion and improving inference accuracy. Additionally, we apply our approach to two real datasets collected from the human gut and vagina, respectively, demonstrating the wide applicability of our methods. The results highlight the efficacy of our covariance estimators in addressing the challenges of microbiome data analysis. The corresponding software implementation is publicly available at https://github.com/yimshi/robustestimates. [ABSTRACT FROM AUTHOR]

The complex nature of microbiome data has made the differential abundance analysis challenging. Microbiome abundance counts are often skewed to the right and heteroscedastic (also known as overdispersion), potentially leading to incorrect inferences if not properly addressed. In this paper, we propose a simple yet effective framework to tackle the challenges by integrating Poisson (loglinear) regression with standard error estimation through the Bootstrap method and Sandwich robust estimation. Such standard error estimates are accurate and yield satisfactory inference even if the distributional assumption or the variance structure is incorrect. Our approach is validated through extensive simulation studies, demonstrating its effectiveness in addressing overdispersion and improving inference accuracy. Additionally, we apply our approach to two real datasets collected from the human gut and vagina, respectively, demonstrating the wide applicability of our methods. The results highlight the efficacy of our covariance estimators in addressing the challenges of microbiome data analysis. The corresponding software implementation is publicly available at https://github.com/yimshi/robustestimates. [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]

Purpose: Muscle, tendon, and muscle–tendon unit (MTU) stiffness as well as passive peak torque (PPT) or delayed stretching pain sensation are typical explanatory approaches for stretching adaptations. However, in literature, differences in the study inclusion, as well as applying meta-analytical models without accounting for intrastudy dependency of multiple and heteroscedasticity of data bias the current evidence. Furthermore, most of the recent analyses neglected to investigate PPT adaptations and further moderators. Methods: The presented review used the recommended meta-analytical calculation method to investigate the effects of stretching on stiffness as well as on passive torque parameters using subgroup analyses for stretching types, stretching duration, and supervision. Results: Chronic stretching reduced muscle stiffness (− 0.38, p = 0.01) overall, and also for the supervised (− 0.49, p = 0.004) and long static stretching interventions (− 0.61, p < 0.001), while the unsupervised and short duration subgroups did not reach the level of significance (p = 0.21, 0.29). No effects were observed for tendon stiffness or for subgroups (e.g., long-stretching durations). Chronic PPT (0.55, p = 0.005) in end ROM increased. Only long-stretching durations sufficiently decreased muscle stiffness acutely. No effects could be observed for acute PPT. Conclusion: While partially in accordance with previous literature, the results underline the relevance of long-stretching durations when inducing changes in passive properties. Only four acute PPT in end ROM studies were eligible, while a large number were excluded as they provided mathematical models and/or lacked control conditions, calling for further randomized controlled trials on acute PPT effects. [ABSTRACT FROM AUTHOR]

Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its variations have been widely adopted in the study of financial volatilities, while the extension of GARCH‐type models to high‐dimensional data is always difficult because of over‐parameterization and computational complexity. In this article, we propose a multi‐variate GARCH‐type model that can simplify the parameterization by utilizing the network structure that can be appropriately specified for certain types of high‐dimensional data. The asymmetry in the dynamics of volatilities is also considered as our model adopts a threshold structure. To enable our model to handle data with extremely high dimension, we investigate the near‐epoch dependence (NED) of our model, and the asymptotic properties of our quasi‐maximum‐likelihood‐estimator (QMLE) are derived from the limit theorems for NED random fields. Simulations are conducted to test our theoretical results. At last we fit our model to log‐returns of four groups of stocks and the results indicate that bad news is not necessarily more influential on volatility if the network effects are considered. [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]

This paper considers the problem of deriving heteroskedasticity and autocorrelation robust (HAR) inference about a scalar parameter of interest. The main assumption is that there is a known upper bound on the degree of persistence in data. I derive finite‐sample optimal tests in the Gaussian location model and show that the robustness‐efficiency tradeoffs embedded in the optimal tests are essentially determined by the maximal persistence. I find that with an appropriate adjustment to the critical value, it is nearly optimal to use the so‐called equal‐weighted cosine (EWC) test, where the long‐run variance is estimated by projections onto q type II cosines. The practical implications are an explicit link between the choice of q and assumptions on the underlying persistence, as well as a corresponding adjustment to the usual Student‐t critical value. I illustrate the results in two empirical examples. [ABSTRACT FROM AUTHOR]

Are corporate earnings (CE) announcements important for economic activity? We address this question using a novel identification method that combines the valuable information from CE announcements with the heteroscedasticity of shocks experienced on these particular days. Our results demonstrate that CE announcements have a significant impact on the macroeconomy, exhibiting dynamics similar to traditional financial disruptions. We establish that CE announcements' shocks can be classified as financial shocks, highlighting their critical role in the financial system. [ABSTRACT FROM AUTHOR]

This study examines whether the disposition effect can explain time‐varying risk preference and predict the equity risk premium. To do so, we propose an augmented general autoregressive conditional heteroskedasticity (GARCH)‐in‐Mean model unraveling the complex relationship between unrealized gains/losses, realized returns, and the equity risk premium. In our model, the risk aversion coefficient varies with the market state of unrealized gains/losses. Using data from the US stock markets, we show strong evidence that the disposition effect drives time‐varying risk preference: The risk aversion coefficient is significantly positive during periods of unrealized gains, but insignificant during periods of unrealized losses. These findings reconcile the conflicting results of the risk‐return trade‐off in existing literature. Moreover, our model shows significant predictability of the equity risk premium, both in‐sample and out‐of‐sample. Incorporating our model's predictions can yield substantial utility gains for a mean‐variance investor. Our results indicate that the disposition effect leads to time‐varying risk preference and thus induces equity risk premium predictability. [ABSTRACT FROM AUTHOR]

We provide a new estimation method for conditional moment models via the martingale difference divergence (MDD). Our MDD‐based estimation method is formed in the framework of a continuum of unconditional moment restrictions. Unlike the existing estimation methods in this framework, the MDD‐based estimation method adopts a non‐integrable weighting function, which could capture more information from unconditional moment restrictions than the integrable weighting function to enhance the estimation efficiency. Due to the nature of shift‐invariance in MDD, our MDD‐based estimation method can not identify the intercept parameters. To overcome this identification issue, we further provide a two‐step estimation procedure for the model with intercept parameters. Under regularity conditions, we establish the asymptotics of the proposed estimators, which are not only easy‐to‐implement with expectation‐based asymptotic variances, but also applicable to time series data with an unspecified form of conditional heteroskedasticity. Finally, we illustrate the usefulness of the proposed estimators by simulations and two real examples. [ABSTRACT FROM AUTHOR]

We propose a new class of modified regression‐based tests for detecting asset price bubbles designed to be robust to the presence of general forms of both conditional and unconditional heteroskedasticity in the price series. This modification, based on the approach developed in Beare (2018) in the context of conventional unit root testing, is achieved by purging the impact of unconditional heteroskedasticity from the data using a kernel estimate of volatility before the application of the bubble detection methods proposed in Phillips, Shi and Yu (2015) (PSY). The modified statistic is shown to achieve the same limiting null distribution as the corresponding (heteroskedasticity‐uncorrected) statistic from PSY would obtain under homoskedasticity, such that the usual critical values provided in PSY may still be used. Versions of the test based on regressions including either no intercept or a (redundant) intercept are considered. Representations for asymptotic local power against a single bubble model are also derived. Monte Carlo simulation results highlight that neither one of these tests dominates the other across different bubble locations and magnitudes, and across different models of time‐varying volatility. Accordingly, we also propose a test based on a union of rejections between the with‐ and without‐intercept variants of the modified PSY test. The union procedure is shown to perform almost as well as the better of the constituent tests for a given DGP, and also performs very well compared to existing heteroskedasticity‐robust tests across a large range of simulation DGPs. [ABSTRACT FROM AUTHOR]

Residuals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and Poisson distributions, due to heteroscedasticity and dependence among observations. This article introduces a novel standardized combined residual for linear and nonlinear regression models within the exponential family. By integrating information from both the mean and dispersion sub-models, the new residual provides a unified diagnostic tool that enhances computational efficiency and eliminates the need for projection matrices. Simulation studies and real-world applications demonstrate its advantages in efficiency and interpretability over traditional residuals. [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]

When investigating unobservable, complex traits, data collection and aggregation processes can introduce distinctive features to the data such as boundedness, measurement error, clustering, outliers, and heteroscedasticity. Failure to collectively address these features can result in statistical challenges that prevent the investigation of hypotheses regarding these traits. This study aimed to demonstrate the efficacy of the Bayesian beta-proportion generalized linear latent and mixed model (beta-proportion GLLAMM) (Rabe-Hesketh et al., Psychometrika, 69(2), 167–90, 2004a, Journal of Econometrics, 128(2), 301–23, 2004c, 2004b; Skrondal and Rabe-Hesketh 2004) in handling data features when exploring research hypotheses concerning speech intelligibility. To achieve this objective, the study reexamined data from transcriptions of spontaneous speech samples initially collected by Boonen et al. (Journal of Child Language, 50(1), 78–103, 2023). The data were aggregated into entropy scores. The research compared the prediction accuracy of the beta-proportion GLLAMM with the normal linear mixed model (LMM) (Holmes et al., 2019) and investigated its capacity to estimate a latent intelligibility from entropy scores. The study also illustrated how hypotheses concerning the impact of speaker-related factors on intelligibility can be explored with the proposed model. The beta-proportion GLLAMM was not free of challenges; its implementation required formulating assumptions about the data-generating process and knowledge of probabilistic programming languages, both central to Bayesian methods. Nevertheless, results indicated the superiority of the model in predicting empirical phenomena over the normal LMM, and its ability to quantify a latent potential intelligibility. Additionally, the proposed model facilitated the exploration of hypotheses concerning speaker-related factors and intelligibility. Ultimately, this research has implications for researchers and data analysts interested in quantitatively measuring intricate, unobservable constructs while accurately predicting the empirical phenomena. [ABSTRACT FROM AUTHOR]

This paper aims to leverage Bayesian nonlinear expectations to construct Bayesian lower and upper estimates for prices of Ether options, that is, options written on Ethereum, with conditional heteroscedasticity and model uncertainty. Specifically, a discrete-time generalized conditional autoregressive heteroscedastic (GARCH) model is used to incorporate conditional heteroscedasticity in the logarithmic returns of Ethereum, and Bayesian nonlinear expectations are adopted to introduce model uncertainty, or ambiguity, about the conditional mean and volatility of the logarithmic returns of Ethereum. Extended Girsanov's principle is employed to change probability measures for introducing a family of alternative GARCH models and their risk-neutral counterparts. The Bayesian credible intervals for "uncertain" drift and volatility parameters obtained from conjugate priors and residuals obtained from the estimated GARCH model are used to construct Bayesian superlinear and sublinear expectations giving the Bayesian lower and upper estimates for the price of an Ether option, respectively. Empirical and simulation studies are provided using real data on Ethereum in AUD. Comparisons with a model incorporating conditional heteroscedasticity only and a model capturing ambiguity only are presented. [ABSTRACT FROM AUTHOR]

We present a Bayesian approach for the analysis of rating data when a scaling component is taken into account, thus incorporating a specific form of heteroskedasticity. Model-based probability effect measures for comparing distributions of several groups, adjusted for explanatory variables affecting both location and scale components, are proposed. Markov Chain Monte Carlo techniques are implemented to obtain parameter estimates of the fitted model and the associated effect measures. An analysis on students' evaluation of a university curriculum counselling service is carried out to assess the performance of the method and demonstrate its valuable support for the decision-making process. [ABSTRACT FROM AUTHOR]

We propose a model for interval-valued time series that specifies the conditional joint distribution of the upper and lower bounds as a mixture of truncated bivariate normal distributions. It preserves the interval natural order and provides great flexibility on capturing potential conditional heteroscedasticity and non-Gaussian features. The standard expectation maximization (EM) algorithm applied to truncated mixtures does not provide a closed-form solution in the M step. A new EM algorithm solves this problem. The model applied to the interval-valued IBM daily stock returns exhibits superior performance over competing models in-sample and out-of-sample evaluation. A trading strategy showcases the usefulness of our approach. [ABSTRACT FROM AUTHOR]

We study two sources of heteroscedasticity in high-frequency financial data and estimate their contribution to overall volatility by means of a Markov switching (MS) structural VAR model. We achieve identification for all coefficients by assuming that the structural errors follow a GARCH-DCC process. Using transaction data of the EUR/USD interdealer market in 2016, we first detect three regimesof volatility. Then we show that both sources of volatility matter for the transmission of shocks, and that information is channeled to the market mostly through demand shocks. This suggests that, on the EUR/USD market, some liquidity takers (LTs) are better informed than both liquidity providers and those LTs who follow a feedback strategy. [ABSTRACT FROM AUTHOR]

Abstract Background A platform trial approach allows adding arms to on-going trials to speed up intervention discovery programs. A control arm remains open for recruitment in a platform trial while intervention arms may be added after the onset of the study and could be terminated early for efficacy and/or futility when early stopping is allowed. The topic of utilising non-concurrent control data in the analysis of platform trials has been explored and discussed extensively. A less familiar issue is the presence of heterogeneity, which may exist for example due to modification of enrolment criteria and recruitment strategy. Method We conduct a simulation study to explore the impact of heterogeneity on the analysis of a two-stage platform trial design. We consider heterogeneity in treatment effects and heteroscedasticity in outcome data across stages for a normally distributed endpoint. We examine the performance of some hypothesis testing procedures and modelling strategies. The use of non-concurrent control data is also considered accordingly. Alongside standard regression analysis, we examine the performance of a novel method that was known as the pairwise trials analysis. It is similar to a network meta-analysis approach but adjusts for treatment comparisons instead of individual studies using fixed effects. Results Several testing strategies with concurrent control data seem to control the type I error rate at the required level when there is heteroscedasticity in outcome data across stages and/or a random cohort effect. The main parameter of treatment effects in some analysis models correspond to overall treatment effects weighted by stage wise sample sizes; while others correspond to the effect observed within a single stage. The characteristics of the estimates are not affected significantly by the presence of a random cohort effect and/ or heteroscedasticity. Conclusion In view of heterogeneity in treatment effect across stages, the specification of null hypotheses in platform trials may need to be more subtle. We suggest employing testing procedure of adaptive design as opposed to testing the statistics from regression models; comparing the estimates from the pairwise trials analysis method and the regression model with interaction terms may indicate if heterogeneity is negligible.

In efficacy and safety studies, a vital research concern is to determine the therapeutic window of a pharmaceutical compound. The approach to finding minimum effective dose and maximum safe dose involves multiple comparisons. Generally, in such a problem, a family‐wise error rate is inherited if multiplicity adjustment is not handled properly. This article without a need for multiplicity adjustment formulates a stepwise confidence interval method to identify a therapeutic window of a pharmaceutical compound when equality of variances cannot be assumed and when ratios of variances are known. This article employed Fieller's method and obtained individual confidence intervals for the identification of the minimum effective dose and maximum safe dose. A simulation study was performed and the results show that the confidence interval method proposed in this article controls the family‐wise error rate strongly. Power increases whenever the ratio of means increases and decreases against higher clinical relevance margins. The proposed procedure was applied to real data and provided optimum results. It was also observed that as both the ratio of means and the sample sizes increase, power increases accordingly. [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 aims to investigate the role of accounting comparability in firm investment efficiency of firms in China. Using a sample of listed firms in China's A-share market from 2005 to 2016, this study empirically categorizes the firms into two groups based on overinvestment and underinvestment. After implementing several tests including those for collinearity and heteroskedasticity, the primary results of the empirical models show that accounting comparability can only improve the efficiency of a company's investment in terms of reducing the overinvestment and increasing the underinvestment through the impact of a financing constraint on the overinvestment and underinvestment. This study thus suggests that the Chinese authorities should take steps to ensure that firms increase the extent of their accounting comparability with other firms, thereby making their accounting statements more comparable not only in the same industry, but also in different industries in accordance with the official accounting regulations and by adopting the same definitions for accounting indicators. [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]

We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular, it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of an experiment. [ABSTRACT FROM AUTHOR]

Multilevel modeling (MLM) is commonly used in psychological research to model clustered data. However, data in applied research usually violate one of the essential assumptions of MLM—homogeneity of variance. While the fixed-effect estimates produced by the maximum likelihood method remain unbiased, the standard errors for the fixed effects are misestimated, resulting in inaccurate inferences and inflated or deflated type I error rates. To correct the bias in fixed effects standard errors and provide valid inferences, small-sample corrections such as the Kenward-Roger (KR) adjustment and the adjusted cluster-robust standard errors (CR-SEs) with the Satterthwaite approximation for t tests have been used. The current study compares KR with random slope (RS) models and the adjusted CR-SEs with ordinary least squares (OLS), random intercept (RI) and RS models to analyze small, heteroscedastic, clustered data using a Monte Carlo simulation. Results show the KR procedure with RS models has large biases and inflated type I error rates for between-cluster effects in the presence of level 2 heteroscedasticity. In contrast, the adjusted CR-SEs generally yield results with acceptable biases and maintain type I error rates close to the nominal level for all examined models. Thus, when the interest is only in within-cluster effect, any model with the adjusted CR-SEs could be used. However, when the interest is to make accurate inferences of the between-cluster effect, researchers should use the adjusted CR-SEs with RS to have higher power and guard against unmodeled heterogeneity. We reanalyzed an example in Snijders & Bosker (2012) to demonstrate the use of the adjusted CR-SEs with different models. [ABSTRACT FROM AUTHOR]

Measuring stock market volatility and its determinants is critical for stock market participants, as volatility spillover effects affect corporate performance. This study adopted a novel approach to analysing and implementing GARCH-MIDAS modelling methods. The classical GARCH as a benchmark and the univariate GARCHMIDAS framework are the GARCH family models whose forecasting outcomes are examined. The outcome of GARCH-MIDAS analyses suggests that inflation, interest rate, exchange rate, and oil price are significant determinants of the volatility of the Johannesburg Stock Market All Share Index. While for Nigeria, the volatility reacts significantly to the exchange rate and oil price. Furthermore, inflation, exchange rate, interest rate, and oil price significantly influence Ghanaian equity volatility, especially for the long-term volatility component. The significant shock of the oil price and exchange rate to volatility is present in all three markets using the generalized autoregressive conditional heteroscedastic-mixed data sampling (GARCH-MIDAS) framework. The GARCH-MIDAS, with a powerful fusion of the GARCH model’s volatility-capturing capabilities and the MIDAS approach’s ability to handle mixed-frequency data, predicts the volatility for all variables better than the traditional GARCH framework. Incorporating these two techniques provides an innovative and comprehensive approach to modelling stock returns, making it an extremely useful tool for researchers, financial analysts, and investors. [ABSTRACT FROM AUTHOR]

Mendelian randomization (MR) addresses causal questions using genetic variants as instrumental variables. We propose a new MR method, G-Estimation under No Interaction with Unmeasured Selection (GENIUS)-MAny Weak Invalid IV, which simultaneously addresses the 2 salient challenges in MR: many weak instruments and widespread horizontal pleiotropy. Similar to MR-GENIUS, we use heteroscedasticity of the exposure to identify the treatment effect. We derive influence functions of the treatment effect, and then we construct a continuous updating estimator and establish its asymptotic properties under a many weak invalid instruments asymptotic regime by developing novel semiparametric theory. We also provide a measure of weak identification, an overidentification test, and a graphical diagnostic tool. [ABSTRACT FROM AUTHOR]

This paper focuses on the factor-augmented panel regression models with missing data and individual-varying factors. A so-called CCEM estimator for the slope coefficient is proposed and its asymptotic properties are investigated under some regularity conditions. Furthermore, a joint test statistic is constructed for serial correlation and heteroscedasticity in the idiosyncratic errors. Under the null hypothesis, the test statistic can be shown to be asymptotically chi-square distributed. Monte Carlo simulation results show that the proposed estimator and test statistic have desired performance in finite samples. [ABSTRACT FROM AUTHOR]

In this article, statistical tests concerning the trend coefficient in cointegrating regressions are addressed for the case when the stochastic regressors have deterministic linear trends. The self‐normalization (SN) approach is adopted for developing inferential methods in the integrated and modified ordinary least squares (IMOLS) estimation framework. Two different self‐normalizers are used to construct the SN test statistics: a functional of the recursive IMOLS estimators and a functional of the IMOLS residuals. These two self‐normalizers produce two SN tests, denoted by TSNϵ and τδ1η^T⊥ respectively. Neither test requires studentization with a heteroskedasticity and autocorrelation consistent (HAC) estimator. A trimming parameter ϵ must be chosen to implement the TSNϵ test, whereas the τδ1η^T⊥ test does not require any tuning parameter. In the simulation, the QSNϵ≡TSNϵ2 test exhibits the smallest size distortion among the inferential methods examined in this article. However, this may come with some loss of power, particularly in small samples. [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]

This article introduces customized screening ensemble with shape‐adaptive quantile regression (CseAQR), a novel probabilistic interval forecasting method built upon the quantile regression model. CseAQR utilizes ensemble learning to perform adaptive quantile regression prediction, which can handle the heteroscedasticity feature in time series data by using a weighted adaptive allocation loss function to enhance the adaptability of the basic quantile regression model on the dataset. The model performance predictor is used to select the optimal ensemble learner combination, assign reasonable adaptive weights to it, and obtain a preliminary prediction interval through weighted aggregation. Combining ensemble learners not only improves the accuracy and robustness of prediction intervals but also ensures the commutativity required for conformal prediction. Finally, the conformal prediction method is applied to locally adjust the prediction interval, constructing a more consistently aligned prediction interval with the actual data on a narrower basis. [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]

This study develops a novel approach for improving stock return volatility forecasts using volatility index information with the entropic tilting technique. Unlike traditional linear heteroskedasticity autoregressive methods with option‐implied information, we first derive predictive densities from traditional models, and then tilt using both the first and second moments of the risk‐neutral distribution, which enables us to capture the nonlinear effect in our specification. The empirical findings demonstrate a substantial enhancement in the forecasting accuracy of all models once the first‐ and second‐moment information is considered, where the improvement is both statistically and economically significant. These results have important implications for risk management in well‐established derivatives markets. [ABSTRACT FROM AUTHOR]

Purpose: Given the difficulties in finding significant exchange rate exposure in the extant literature, this paper attempts to resolve the so-called "exposure puzzle" by investigating whether currency movements have any significant impact on international industry returns. Design/methodology/approach: This paper utilizes the multivariate Generalized AutoRegressive Conditional Heteroskedasticity (MGARCH) methodology to estimate both symmetric and asymmetric exchange rate exposures for each industry common across 12 countries simultaneously. Findings: The empirical results show that exchange rate exposure is not only statistically significant but also economically important based on the estimation of an asymmetric three-factor exposure model using MGARCH methodology. This is an extremely important finding as it suggests that the "exposure puzzle" may not be a puzzle at all once a better methodology is utilized in the estimation. Research limitations/implications: Because this study tries to resolve the exchange rate exposure puzzle by focusing on whether exchange rate movements affect ex-post returns as opposed to ex ante expected returns and given the significant exposures with respect to different risk factors found in the study, it is interesting to see if any of these risk factors commands a risk premium. In other words, a natural extension of this study is to test whether any of these risk factors is priced in international industry returns. Practical implications: The findings of the study have interesting implications for international investors who would like to diversify their portfolios across different industries and are concerned about whether the unexpected movements in the bilateral exchange rates will affect their portfolio returns in addition to its interest rate and world market risk exposures. Originality/value: The study utilizes the MGARCH methodology, which has not been fully exploited in the exchange rate exposure literature. [ABSTRACT FROM AUTHOR]

Summary: Heteroskedasticity is a common feature in empirical time series analysis, and in this paper, we consider the effects of heteroskedasticity on statistical tests for equal forecast accuracy. In such a context, we propose two new Diebold–Mariano‐type tests for equal accuracy that employ nonparametric estimation of the loss differential variance function. We demonstrate that these tests have the potential to achieve power improvements relative to the original Diebold–Mariano test in the presence of heteroskedasticity, for a quite general class of loss differential series. The size validity and potential power superiority of our new tests are studied theoretically and in Monte Carlo simulations. We apply our new tests to competing forecasts of changes in the dollar/sterling exchange rate and find the new tests provide greater evidence of differences in forecast accuracy than the original Diebold–Mariano test, illustrating the value of these new procedures for practitioners. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scale-invariant test for linear hypothesis of mean vectors with heteroscedasticity in high-dimensional settings. Most existing tests impose strong conditions on covariance matrices so that null distributions of their tests are asymptotically normal, which restricts the application of test procedures. However, our proposed test has different null distributions under mild conditions. Additionally, the well-known Welch-Satterthwaite chi-square approximation we adopted can automatically mimic the shapes of the null distributions of the test statistic. The performances of the test are illustrated by simulation and real data in finite samples which show that it has robustness and is more powerful than three competitors. [ABSTRACT FROM AUTHOR]