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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]

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

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

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

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

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

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

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

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

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

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

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

The 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 been proposed in the context of weighted least squares (WLS) to address the issue. Estimation of linear regression model becomes more challenging when the issue of heteroscedasticity is bundled together with the presence of outliers. In the present article, we use a relatively latest approach that is the least squares ratio method to estimate a linear regression model in the presence of heteroscedasticity and outliers. We propose an adaptive version of this technique while taking advantage of some existing adaptive estimators to fix the issue of unknown heteroscedasticity. A Monte Carlo evidence has been presented for the performance of the stated estimator varying degree of heteroscedasticity and number of outliers. [ABSTRACT FROM AUTHOR]

This research compares the symmetric and asymmetric effects of generalized autoregressive conditional heteroscedasticity (GARCH)-type models to investigate the volatility of the autoregressive fractionally integrated moving average (ARFIMA) model using the monthly Brent crude oil price series for the period of January 1979–July 2019. The best model of volatility is determined by comparing 13 hybrid models of GARCH (sGARCH, fGARCH, EGARCH, TGARCH, IGARCH, AVGARCH, NGARCH, NAGARCH, APARCH, apARCH, GJRGARCH, gjrGARCH, and csGARCH) in terms of symmetric and asymmetric effects at the level of (1,1). R/S analysis is used to achieve this target. The aggregated variance method, the Higuchi method, and the structural break test are performed to determine the presence of long memory in the dataset. Furthermore, the Hurst exponent method and the Geweke and Porter–Hudak method are used to estimate the fractional difference values. The ARFIMA(2,0.3589648,2)–IGARCH(1,1) model under normal distribution is selected as the best model based on the Akaike information criterion, Schwartz Bayesian information criterion, and by the smallest value for root-mean-squared error, in which this model can be used to predict more accurately than other models. [ABSTRACT FROM AUTHOR]

The aim of this paper is to appraise if there is any improvement subtracting the effects of outliers from existing heteroscedastic models and whether this improvement makes difference with the existing models in achieving efficiency in capturing excess kurtosis in the returns series. The study employed both existing and outlier modified autoregressive conditional heteroscedastic (ARCH), generalized autoregressive conditional heteroscedastic (GARCH), exponential GARCH (EGARCH), Glosten, Jagnnathan and Runkle GARCH (GJR-GARCH) models with respect to normal and student-t distributions to assess the portion of excess kurtosis of the returns series expressed compare to the theoretical value of kurtosis. The data applied were the share prices of Union bank of Nigeria and Unity bank from January 3, 2006 to November 24, 2016, comprising 2690 observations and were obtained from Nigerian Stock Exchange. The results obtained revealed that the Outlier Modified GARCH-type models chosen were adequate and sufficiently reducing the value of excess kurtosis in close proximity to the theoretical value. Therefore, the modification of existing GARCH-type models by subtracting the effects of outliers seems to show a substantive improvement in the portion of excess kurtosis captured and thus proves that the Outlier Modified GARCH-type models make difference with the existing ones. [ABSTRACT FROM AUTHOR]

Aiming at minimizing the ratio of error with respect to the response variable, the least squares ratio is a relatively new method for estimating the regression parameters. In the current article, the performance of this new approach is compared with the traditional OLS approach in the case when homoscedasticity of errors assumption is violated. A comparison is made through a simulation study using mean square error, mean absolute percentage error, and false acceptance rate as performance measures. It is observed that the least square ratio method outperforms the OLS method in case of moderate or severe heteroscedasticity for all sample sizes and in case of weak or mild heteroscedasticity for relatively small samples. Generally, it is noted that the efficiency of the least squares ratio method increases with an increase in the severity of heteroscedasticity as well as an increase in values of common error variance. The use of the least squares ratio method is recommended in case of mild or moderate to severe heteroscedasticity. Similar results were obtained from two real-life examples. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the asymptotic normality of wavelet estimators in the heteroscedastic regression model with φ-mixing errors. Under some suitable conditions, the asymptotic normality of the wavelet estimators of g and f in the heteroscedastic regression model with φ-mixing errors are obtained, which generalize or improve the corresponding ones for α-mixing random variables and martingale difference sequence in some sense. Also, the simulation study of the finite samples provided in this paper shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, a univariate finite mixed generalized normal distribution (MixGND) is proposed. First, we derive some probabilistic properties including hazard rate function, characteristic function, kurtosis and skewness, for a mixture of two generalized normal distributions. In particular, we use a geometric analysis and numerical simulation technique to study the monotonicity of skewness and kurtosis from prescribing corresponding parameters. Then moment estimation and maximum likelihood estimation of parameters are also given. To use the maximum likelihood estimation (MLE) method, an expectation conditional maximization (ECM) algorithm is proposed to estimate and numerically simulate seven parameters of a two-component MixGND under the same variance and heteroscedasticity. By using data sets of the S&P 500 and Shanghai Stock Exchange Composite Index (SSEC), we compare goodness-of-fit performance between the mixture of two generalized normal distributions and the mixture of two normal distributions. The empirical analysis results show that the former better describes the heavy-tailed and leptokurtic characteristics of the daily returns. [ABSTRACT FROM AUTHOR]

Assumption of the classical linear regression model states that the disturbances should have a constant (equal) variance. When this requirement is not met, the loss in efficiency in using ordinary least squares may be substantial and the biases in estimated standard errors may lead to invalid inferences. This problem is known as heteroscedasticity. There are many tests for heteroscedasticity, we want to know which test is more powerful. We use Monte Carlo simulation to compare the power of seven most commonly used tests for detecting heteroscedasticity, namely, Breusch–Pagan test, Glejser test, Goldfeld–Quandt test, Harvey–Godfrey test, Harrison–McCabe test, Park test, and White test for six common types of heteroscedasticity. Simulation results show that the Harrison–McCabe test has generally the most power in all of the six common types of heteroscedasticity and the White test has generally the least power in all of the six common types of heteroscedasticity. [ABSTRACT FROM AUTHOR]

Traditional pretests to prove homoscedasticity (e.g., Levene's or Bartlett's test) before applying normal parametric techniques like the Student's t test should be avoided: Given the form of their null and alternative hypotheses, they are methodologically inadequate to this end and induce overall (regarding the full testing process, pretesting included) alterations in Type I Error Probability (TIEP). Under normality, not pretesting and always applying the Welch's test (instead of Student's test) or pretesting with the Wellek's equivalence test of heteroscedasticity irrelevance, are more affordable strategies. Here we investigate the robustness, in front of non-normality, of five strategies dealing with possible heteroscedasticity: Pretesting with Levene, F and Wellek's, and applying either the Student's or the Welch's test directly without pretest. Non-normality is simulated by varying degrees of skewness and kurtosis, for distributions inside the Fleishman's system. Robustness is measured in terms of overall TIEP proximity to the nominal significance level. The direct use of Welch's test or pretesting with the Wellek's test are still the most robust approaches, although high degrees of contamination of normality affect them considerably. All approaches improve with growing sample sizes and worsen with unbalancing, but differences still persist, in general favoring the above mentioned two approaches. [ABSTRACT FROM AUTHOR]

The use of Almon technique is very common for the estimation of distributed lag model (DLM) to encounter the problems stemming due to direct application of the ordinary least squares (OLS) method to this model. However, the Almon estimator may suffer from the problem of multicollinearity as the constructed regressors in the Almon technique may be plagued with considerable degree of multicollinearity. To address this issue, the use of Almon-ridge estimator (ARE) has been considered as an alternative method for the estimation of DLM by many authors. In addition, the DLM may also face the problem of heteroscedasticity that may result in inconsistent covariance matrix estimator of ARE, leading to invalid testing inference about parameters of the DLM. In the present article, we propose to use the robust covariance matrix estimators of ARE for providing valid inference about parameters of the DLM taking multicollinearity and heteroscedasticity into account. These covariance estimators are used to construct confidence intervals, t- and F-tests. The performance of these confidence intervals and tests is evaluated empirically through the Monte Carlo simulations. The simulation results reveal an attractive performance of the proposed covariance matrix estimators. [ABSTRACT FROM AUTHOR]

To understand the dynamic relationship of discrete time series processes, we adopted copula directional dependence via beta regression model applied with generalized autoregressive conditional heteroscedasticity (INGARCH) marginals. To validate the proposed method, we completed simulations of two INGARCH processes from asymmetric bivariate copula function with members such as Gaussian and Plackett copula functions. The simulations show that the proposed method is consistent for deriving directional dependent measurements regardless of the choice of the symmetric members. The proposed method is applied to the bivariate discrete time series data of the monthly counts of sandstorms and dust haze phenomena in Saudi Arabia. [ABSTRACT FROM AUTHOR]

The use of penalized least squares based estimations in high dimensional linear regression has been received a great deal of attention during past decades and applied to variable selections under sparsity scenarios. However, it remains unclear that complex data with multiple uncertainties in measurements, such as outliers, error-in-variables and heteroscedasticity, to what extent, can influence these approaches. This paper, here, demonstrates the behaviors of least-squares based approaches in complex data problems, and suggests an alternative approach, Wald-type estimator, relying on theoretical perspectives. Numerical experiments and real data analysis are also presented to illustrate the performance of the different estimation strategies. [ABSTRACT FROM AUTHOR]

A transformation of the Welch statistic to compare means is proposed to correct skewness and kurtosis of parent populations. The results show that this transformation seems to improve the performance of the test in heavy-tailed distributions more than other transformations focused only on skewness. The proposed test outperforms the Welch test in asymmetric heavy-tailed distributions with high heteroscedasticity and it behaves better than the Johnson's transformation trimmed mean Welch test in normal, near-normal and light-tailed distributions. It may also be a better option when some of the distributions are heavy-tailed and some light-tailed. [ABSTRACT FROM AUTHOR]

This work considers conditionally heteroscedastic time series with possibly asymmetric errors (e.g., skewed t-distributions). Suppose that the error distribution is unknown and estimating functions, so called quasi-likelihood (QL) scores are employed to estimate parameters. The quasi-likelihood can be regarded as a special case of the Godambe's optimum estimating functions (see, e.g., Hwang and Basawa (2011)). To capture asymmetry in errors, a threshold-innovation is newly suggested to construct an "optimum" quasi likelihood score. It is shown that the threshold innovation is "better" than the standard innovation especially when errors are asymmetrically distributed. A simulation study is reported and a real data analysis is illustrated. [ABSTRACT FROM AUTHOR]

In the field of ranking and selection, the quality engineer would like to compare the mean lifetimes of several treatment populations with the control for exponential distribution. In most cases, the scale parameters are unknown and unequal. We proposed a one-stage multiple comparison procedure for comparing k-1 treatment exponential mean lifetimes with the control based on doubly censored samples under heteroscedasticity. The tables of critical values for the multiple comparison procedures are listed for the practical use. At last, one example of duration of remission for 20 patients each taking one of four drugs for the treatment of leukemia is given to demonstrate the application of our proposed method. [ABSTRACT FROM AUTHOR]

We consider the detection of marginal heteroscedasticity for partial linear single-index models. We regress absolute values of residuals on each covariate by marginal univariate nonparametric smoothing with a sequence of bandwidths, then a ordinary least squares estimator between the quadratic nonparametric estimate and bandwidths are obtained. We rank least squares estimates and obtain the top ranked covariates according to a ridge-type absolute coefficient ratio. Then, a refinement step is based to the smoothly clipped absolute deviation penalization method for marginal heteroscedastic detection. Simulation studies and a real dataset are conducted to demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the problem of estimating the model error distribution in a heteroscedastic varying coefficient regression model is considered. A residual-based estimator of the model error distribution is proposed, associated with its asymptotic results. Furthermore, the application of estimated error distribution for testing whether some varying coefficient components are constants or not is investigated. Test statistics based on the Kolmogorov-Smirnov and Cramér-von Mises type functionals of the estimated model error distribution are used to check the null hypothesis. A bootstrap procedure is further proposed to calculate the critical values. Simulation studies are conducted to demonstrate the performance of the proposed test statistics. [ABSTRACT FROM AUTHOR]

The estimation of variance function plays an extremely important role in statistical inference of the regression models. In this paper we propose a variance modelling method for constructing the variance structure via combining the exponential polynomial modelling method and the kernel smoothing technique. A simple estimation method for the parameters in heteroscedastic linear regression models is developed when the covariance matrix is unknown diagonal and the variance function is a positive function of the mean. The consistency and asymptotic normality of the resulting estimators are established under some mild assumptions. In particular, a simple version of bootstrap test is adapted to test misspecification of the variance function. Some Monte Carlo simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by the ozone concentration dataset. [ABSTRACT FROM AUTHOR]

Alternatives for positively skewed and heteroscedastic data include the Yuen-Welch (YW) test, data transformations, and the generalized linear model (GzLM). Because the GzLM is rarely considered in psychology compared to the other two, we compared these strategies conceptually and empirically. The YW test generally has satisfactory power, but its trimmed mean can deviate substantially from the arithmetic mean, which is often the desired parameter. The gamma GzLM can be used as a substitute for the log transformation and addresses the limitations in inference for the YW and data transformations. [ABSTRACT FROM AUTHOR]

In this paper, a modified one-stage multiple comparison procedures with a control for exponential location parameters based on the doubly censored sample under heteroscedasticity is proposed. A simulation study is done and the results show that the proposed procedures have shorter confidence length with coverage probabilities closer to the nominal ones compared with the one proposed in Wu (2017). At last, an example of comparing the duration of remission for four drugs as the treatment of leukemia is given to demonstrate the proposed procedures. [ABSTRACT FROM AUTHOR]

We propose a four-parameter extended generalized gamma model, which includes as special cases some important distributions and it is very useful for modeling lifetime data. A advantage is that it can represent the error distribution for a new heteroscedastic log-odd log-logistic generalized gamma regression model. The proposed heteroscedastic regression model can be used more effectively in the analysis of survival data since it includes as special models several widely-known regression models. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. Overall, the new regression model is very useful to the analysis of real data. [ABSTRACT FROM AUTHOR]

This paper proposes estimators of the first-order autocorrelation that are based on suitably transformed ratios of successive observations. The new estimators are given by simple functions of the observations. Numerical optimization is not required. Simulations show that they are highly robust against extreme values and clusters of high volatility and are therefore particularly useful for the estimation of serial correlation in return series. Besides, the results of the simulation study also call into question the common practice of correcting the small-sample bias of conventional estimators. [ABSTRACT FROM AUTHOR]

Symmetric kernel smoothing is commonly used in estimating the nonparametric component in the partial linear regression models. In this article, we propose a new estimation method for the partial linear regression models using the inverse Gaussian kernel when the explanatory variable of the nonparametric component is non-negatively supported. As an asymmetric kernel function, the inverse Gaussian kernel is also supported on the non-negative half line. The asymptotic properties, including the asymptotic normality, uniform almost sure convergence, and the iterated logarithm laws, of the proposed estimators are thoroughly discussed for both homoscedastic and heteroscedastic cases. The simulation study is conducted to evaluate the finite sample performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

In this paper, we present one-stage multiple comparisons for exponential mean lifetimes with the control under heteroscedasticity including one-sided and two-sided confidence intervals. These intervals can be used to identify a subset which includes all noworse- than-the-control treatments in an experimental design and to identify better-than-the-control, worse-than-the- control and notmuch- different-from-the-control products in agriculture, stock market, pharmaceutical industries in terms of the mean lifetimes. Tables of critical values are obtained using the technique given in (Lam, 1988, 1992), An example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures. [ABSTRACT FROM AUTHOR]

Heteroscedastic measurement error models are widely used in epidemiological, analytical chemistry, and other research areas. In this article, we propose a heteroscedastic measurement error model for replicated data under scale mixtures of normal distributions with/without equation error, which covers unpair and/or unequal replication cases. We obtain iterative formulas of maximum likelihood estimations via EM algorithm, and provide closed forms of asymptotic variances of the estimators. Simulation studies and a real data application are reported to investigate the effective and robust performances of the model and estimates. [ABSTRACT FROM AUTHOR]

In this article, a new class of variance function estimators is proposed in the setting of heteroscedastic nonparametric regression models. To obtain a variance function estimator, the main proposal is to smooth the product of the response variable and residuals as opposed to the squared residuals. The asymptotic properties of the proposed methodology are investigated in order to compare its asymptotic behavior with that of the existing methods. The finite sample performance of the proposed estimator is studied through simulation studies. The effect of the curvature of the mean function on its finite sample behavior is also discussed. [ABSTRACT FROM AUTHOR]

To study the equality of regression coefficients in several heteroscedastic regression models, we propose a fiducial-based test, and theoretically examine the frequency property of the proposed test. We numerically compare the performance of the proposed approach with the parametric bootstrap (PB) approach. Simulation results indicate that the fiducial approach controls the Type I error rates satisfactorily regardless of the number of regression models and sample sizes, whereas the PB approach tends to be a little of liberal in some scenarios. Finally, the proposed approach is applied to an analysis of a real dataset for illustration. [ABSTRACT FROM PUBLISHER]

This article proposes a new directional dependence by using the Gaussian copula beta regression model. In particular, we consider an asymmetric Generalized AutoRegressive Conditional Heteroscedasticity (GARCH) model for the marginal distribution of standardized residuals to make data exhibiting conditionally heteroscedasticity to white noise process. With the simulated data generated by an asymmetric bivariate copula, we verify our proposed directional dependence method. For the multivariate direction dependence by using the Gaussian copula beta regression model, we employ a three-dimensional archemedian copula to generate trivariate data and then show the directional dependence for one random variable given two other random variables. With West Texas Intermediate Daily Price (WTI) and the Standard & Poor’s 500 (S&P 500), our proposed directional dependence by the Gaussian copula beta regression model reveals that the directional dependence from WTI to S&P 500 is greater than that from S&P 500 to WTI. To validate our empirical result, the Granger causality test is conducted, confirming the same result produced by our method. [ABSTRACT FROM AUTHOR]

Real time series can present anomalies, like non-additivity, non-normality, and heteroscedasticity, which makes using GARMA models impossible. Our article introduces a new class of models called Transformed Generalized Autoregressive Moving Average (TGARMA) models that allow using transformations to guarantee the GARMA assumptions. We present an extensive simulation study of the influence of the transformation on GARMA estimation. We also propose using bootstrap methods to get more information about the distribution of the transformation parameter. We apply the methodology to data related to annual Swedish fertility rates. [ABSTRACT FROM AUTHOR]

This paper compares the performance between regression analysis and a clustering based neural network approach when the data deviates from the homoscedasticity assumption of regression. Heteroskedasticity is a problem that arises in linear regression due to the unequal error variances. One of the methods to deal heteroskedasticity in classical regression theory is weighted least-square regression (WLS). In order to deal the problem of heteroskedasticity, backpropagation neural network is applied. In this context, an algorithm is proposed which is based on robust estimates of location and dispersion matrix that helps in preserving the error assumption of the linear regression. Analysis is carried out with appropriate designs using simulated data and the results are presented. [ABSTRACT FROM AUTHOR]

Extended zero-one inflated beta and adjusted three-part regression models are introduced to analyze proportional response data where there are nonzero probabilities that the response variable takes the values zero and one. The proposed models adapt skewness and heteroscedasticity of the fractional response data, and are constructed to estimate the unknown parameters. Extensive Monte Carlo simulation studies are used to compare the performance of the two approaches with respect to bias and root mean square error. A real data example is presented to illustrate the application of both regression models. [ABSTRACT FROM AUTHOR]

In this article, an extensive Monte Carlo simulation study is conducted to evaluate and compare nonparametric multiple comparison tests under violations of classical analysis of variance assumptions. Simulation space of the Monte Carlo study is composed of 288 different combinations of balanced and unbalanced sample sizes, number of groups, treatment effects, various levels of heterogeneity of variances, dependence between subgroup levels, and skewed error distributions under the single factor experimental design. By this large simulation space, we present a detailed analysis of effects of the violations of assumptions on the performance of nonparametric multiple comparison tests in terms of three error and four power measures. Observations of this study are beneficial to decide the optimal nonparametric test according to requirements and conditions of undertaken experiments. When some of the assumptions of analysis of variance are violated and number of groups is small, use of stepwise Steel-Dwass procedure with Holm's approach is appropriate to control type I error at a desired level. Dunn's method should be employed for greater number of groups. When subgroups are unbalanced and number of groups is small, Nemenyi's procedure with Duncan's approach produces high power values. Conover's procedure successfully provides high power values with a small number of unbalanced groups or with a greater number of balanced or unbalanced groups. At the same time, Conover's procedure is unable to control type I error rates. [ABSTRACT FROM AUTHOR]

We propose a variational mode decomposition approach to estimate the variance function in a nonparametric heteroscedastic fixed design regression model. A data-driven estimator is constructed by applying variational mode decomposition technique to the difference-based initial estimates. The numerical results show that the proposed estimator performs better than the existing variance estimation procedures in the mean square sense. [ABSTRACT FROM AUTHOR]

Distributions of a response y (height, for example) differ with values of a factor t (such as age). Given a response y* for a subject of unknown t*, the objective of inverse prediction is to infer the value of t* and to provide a defensible confidence set for it. Training data provide values of y observed on subjects at known values of t. Models relating the mean and variance of y to t can be formulated as mixed (fixed and random) models in terms of sets of functions of t, such as polynomial spline functions. A confidence set on t* can then be had as those hypothetical values of t for which y* is not detected as an outlier when compared to the model fit to the training data. With nonconstant variance, the p-values for these tests are approximate. This article describes how versatile models for this problem can be formulated in such a way that the computations can be accomplished with widely available software for mixed models, such as SAS PROC MIXED. Coverage probabilities of confidence sets on t* are illustrated in an example. [ABSTRACT FROM AUTHOR]

Heteroscedasticity testing has a long history and is still an important matter in the linear model. There exist many types of tests, but they are limited in use to their own specific cases and sensitive to normality. Here, we propose a dimension test approach to heteroscedasticity. The proposed test overcomes the shortcomings of the existing methods, so that it is robust to normality and is unified in sense that it is applicable in the linear model with multi-dimensional response. Numerical studies confirm that the proposed test is favorable over the existing tests with moderate sample sizes, and real data analysis is presented. [ABSTRACT FROM AUTHOR]

In this article, we consider the Wald test statistic for testing equality between the sets of regression coefficients in two linear regression models when the disturbance variances may possibly be unequal. This test can be also used as a test for a structural break. However, it is well known that the test based on the Wald test statistic suffers from severe size distortion in small sample when the disturbance variances of the two regression models are unequal. Our simulation results show that substantial improvements are made when the bootstrap methods are applied. [ABSTRACT FROM AUTHOR]

The linear regression models with the autoregressive moving average (ARMA) errors (REGARMA models) are often considered, in order to reflect a serial correlation among observations. In this article, we focus on an adaptive least absolute shrinkage and selection operator (LASSO) (ALASSO) method for the variable selection of the REGARMA models and extend it to the linear regression models with the ARMA-generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) errors (REGARMA-GARCH models). This attempt is an extension of the existing ALASSO method for the linear regression models with the AR errors (REGAR models) proposed by Wang et al. in 2007. New ALASSO algorithms are proposed to determine important predictors for the REGARMA and REGARMA-GARCH models. Finally, we provide the simulation results and real data analysis to illustrate our findings. [ABSTRACT FROM AUTHOR]

Between–within models are generalized linear mixed models (GLMMs) for clustered data that incorporate a random intercept together with fixed effects for within-cluster and between-cluster covariates; the between-cluster covariates represent the cluster means of the within-cluster covariates. One popular use of these models is to adjust for confounding of the effect of within-cluster covariates due to unmeasured between-cluster covariates. Previous research has shown via simulations that using this approach can yield inconsistent estimators. We present theory and simulations as evidence that a primary cause of the inconsistency is heteroscedasticity of the linearized version of the GLMM used for estimation. [ABSTRACT FROM AUTHOR]

This article deals with the estimation of the parametric component, which is of primary interest, in the heteroscedastic semi-varying coefficient models. Based on the bootstrap technique,we present a procedure for estimating the parameters, which can provide a reliable approximation to the asymptotic distribution of the profile least-square (PLS) estimator. Furthermore, a bootstrap-type estimator of covariance matrix is developed, which is proved to be a consistent estimator of the covariance matrix. Moreover, some simulation experiments are conducted to evaluate the finite sample performance for the proposed methodology. Finally, the Australia CPI dataset is analyzed to demonstrate the application of the methods. [ABSTRACT FROM AUTHOR]