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In this article, we propose a new regression method called general composite quantile regression (GCQR) which releases the unrealistic finite error variance assumption being imposed by the traditional least squares (LS) method. Unlike the recently proposed composite quantile regression (CQR) method, our proposed GCQR allows any continuous non-uniform density/weight function. As a result, determination of the number of uniform quantile positions is not required. Most importantly, the proposed GCQR criterion can be readily transformed to a linear programing problem, which substantially reduces the computing time. Our theoretical and empirical results show that the GCQR is generally efficient than the CQR and LS if the weight function is appropriately chosen. The oracle properties of the penalized GCQR are also provided. Our simulation results are consistent with the derived theoretical findings. A real data example is analyzed to demonstrate our methodologies. [ABSTRACT FROM AUTHOR]

In longitudinal data analysis, many data features are frequently encountered in practice. For example, variates are usually measured with censoring, substantial errors and non-normal feature, etc. In such case, it is impossible to give a precise result by conducting statistical inference of separate analysis. The joint modeling may be a considerable alternative. The superiority of joint modeling is that it can implement a simultaneous analysis for longitudinal mixed models with random effects, censoring, nor-normal errors, errors in covariates and heavy-tailed feature by pooling all data information together. However, most of traditional modeling methods aim at depicting the average variation of outcome variable conditionally on covariates, which may result in non-robust estimation results when suffering outliers or non-normal errors. Quantile regression provides an attractive alternative to model longitudinal data with multiple data features, which can draw a complete picture of the conditional distributions of outcome variable and bring out robust estimation results. In this paper, we conduct the likelihood-based joint quantile regression for longitudinal mixed models by accounting for the above multiple data features simultaneously. Based on the asymmetric Laplace distribution (ALD), the Monte Carlo Expectation-Maximization (MCEM) algorithm is employed to address the estimation problem. Finally, some Monte Carlo simulations are conducted and an AIDS data analysis is provided to illustrate the developed procedures. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inherent association between mean and covariance in the joint mean–covariance modeling and propose a joint mean–covariance random effect model based on the modified Cholesky decomposition for longitudinal data. Meanwhile, we apply M‐H algorithm to simulate the posterior distributions of model parameters. Besides, a computationally efficient Monte Carlo expectation maximization (MCEM) algorithm is developed for carrying out maximum likelihood estimation. Simulation studies show that the model taking into account the inherent association between mean and covariance has smaller standard deviations of the estimators of parameters, which makes the statistical inferences much more reliable. In the real data analysis, the estimation of parameters in the mean and covariance structure is highly efficient. [ABSTRACT FROM AUTHOR]

Time lag effect exists widely in the course of economic operation. Some economic variables are affected not only by various factors in the current period but also by various factors in the past and even their own past values. As a class of dynamical models, autoregressive distributed lag (ARDL) models are frequently used to conduct dynamic regression analysis. In this paper, we are interested in the quantile regression (QR) modeling of the ARDL model in a dynamic framework. By combining the working likelihood of asymmetric Laplace distribution (ALD) with the expectation–maximization (EM) algorithm into the considered ARDL model, the iterative weighted least square estimators (IWLSE) are derived. Some Monte Carlo simulations are implemented to evaluate the performance of the proposed estimation method. A dataset of the consumption of electricity by residential customers is analyzed to illustrate the application. [ABSTRACT FROM AUTHOR]

This paper considers the quantile regression model with both individual fixed effect and time period effect for general spatial panel data. Fixed effects quantile regression estimators based on instrumental variable method will be proposed. Asymptotic properties of the proposed estimators will be developed. Simulations are conducted to study the performance of the proposed method. We will illustrate our methodologies using a cigarettes demand data set. [ABSTRACT FROM AUTHOR]

Quantile regression (QR) is a natural alternative for depicting the impact of covariates on the conditional distributions of a outcome variable instead of the mean. In this paper, we investigate Bayesian regularized QR for the linear models with autoregressive errors. LASSO-penalized type priors are forced on regression coefficients and autoregressive parameters of the model. Gibbs sampler algorithm is employed to draw the full posterior distributions of unknown parameters. Finally, the proposed procedures are illustrated by some simulation studies and applied to a real data analysis of the electricity consumption. [ABSTRACT FROM AUTHOR]

To get new insights into the adaptability of quantile regression, this paper establishes exact exponential risk bounds (EERB). It shows that these bounds could become the base of the construction of confidence and concentrations sets. In addition, the usual consistency and rate results can also be derived from the risk bounds. It should be mentioned here that: 1) The proposed method has good inherent discontinuous structures that coincides with the true function that does have; 2) When each region has a small number of data points, in practice, the estimate might be unstable. This implies that the homogeneity test and the whole procedure might have some problem in this case; 3) The proposed method does not have boundary effect due to its adaptiveness; 4) Also, the quantile estimates from the proposed method do not suffer from crossing problem; 5) The proposed method is robust to tad behavior of error distributions even when the error terms do not have moments, such as Cauchy distribution; 6) In the simulation, we compare the proposed varying bandwidth kernel smoothing with a local linear smoothing method. Similar results are also available on request against the fixed bandwidth local constant smoothing. [ABSTRACT FROM AUTHOR]

This article presents parametric bootstrap (PB) approaches for hypothesis testing and interval estimation for the regression coefficients and the variance components of panel data regression models with complete panels. The PB pivot variables are proposed based on sufficient statistics of the parameters. On the other hand, we also derive generalized inferences and improved generalized inferences for variance components in this article. Some simulation results are presented to compare the performance of the PB approaches with the generalized inferences. Our studies show that the PB approaches perform satisfactorily for various sample sizes and parameter configurations, and the performance of PB approaches is mostly the same as that of generalized inferences with respect to the expected lengths and powers. The PB inferences have almost exact coverage probabilities and Type I error rates. Furthermore, the PB procedure can be simply carried out by a few simulation steps, and the derivation is easier to understand and to be extended to the incomplete panels. Finally, the proposed approaches are illustrated by using a real data example. [ABSTRACT FROM PUBLISHER]

In this paper, we propose robust randomized quantile regression estimators for the mean and (condition) variance functions of the popular heteroskedastic non parametric regression model. Unlike classical approaches which consider quantile as a fixed quantity, our method treats quantile as a uniformly distributed random variable. Our proposed method can be employed to estimate the error distribution, which could significantly improve prediction results. An automatic bandwidth selection scheme will be discussed. Asymptotic properties and relative efficiencies of the proposed estimators are investigated. Our empirical results show that the proposed estimators work well even for random errors with infinite variances. Various numerical simulations and two real data examples are used to demonstrate our methodologies. [ABSTRACT FROM AUTHOR]

In this article, we consider a generalized linear partially varying-coefficient model for longitudinal data analysis. A local quasi-likelihood method is proposed to estimate the constant-coefficient and varying-coefficient functions simultaneously based on the local polynomial kernel regression. The corresponding standard error estimates are derived. Large sample properties are investigated. The proposed methodologies are demonstrated by extensive simulation studies and a real example. [ABSTRACT FROM PUBLISHER]

Mixture of linear regression models provide a popular treatment for modeling nonlinear regression relationship. The traditional estimation of mixture of regression models is based on Gaussian error assumption. It is well known that such assumption is sensitive to outliers and extreme values. To overcome this issue, a new class of finite mixture of quantile regressions (FMQR) is proposed in this article. Compared with the existing Gaussian mixture regression models, the proposed FMQR model can provide a complete specification on the conditional distribution of response variable for each component. From the likelihood point of view, the FMQR model is equivalent to the finite mixture of regression models based on errors following asymmetric Laplace distribution (ALD), which can be regarded as an extension to the traditional mixture of regression models with normal error terms. An EM algorithm is proposed to obtain the parameter estimates of the FMQR model by combining a hierarchical representation of the ALD. Finally, the iterated weighted least square estimation for each mixture component of the FMQR model is derived. Simulation studies are conducted to illustrate the finite sample performance of the estimation procedure. Analysis of an aphid data set is used to illustrate our methodologies. [ABSTRACT FROM PUBLISHER]

When dealing with regression analysis, heteroscedasticity is a problem that the authors have to face with. Especially if little information can be got in advance, detection of heteroscedasticity as well as estimation of statistical models could be even more difficult. To this end, this paper proposes a quantile difference method (QDM) that can effectively estimate the heteroscedastic function. This method, being completely free from the estimation of mean regression function, is simple, robust and easy to implement. Moreover, the QDM method enables the detection of heteroscedasticity without any restrictions on error terms, consequently being widely applied. What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained. In the end, the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration. [ABSTRACT FROM AUTHOR]

In industrial life tests, reliability analysis and clinical trials, the type-II progressive censoring methodology, which allows for random removals of the remaining survival units at each failure time, has become quite popular for analyzing lifetime data. Parameter estimation under progressively type-II censored samples for many common lifetime distributions has been investigated extensively. However, how to estimate unknown parameters of the mixed distribution models under progressive type-II censoring schemes is still a challenging and interesting problem. Based on progressively type-II censored samples, this paper addresses the estimation problem of mixed generalized exponential distributions. In addition, it is observed that the maximum-likelihood estimates (MLEs) cannot be easily obtained in closed form due to the complexity of the likelihood function. Thus, we make good use of the expectation-maximization algorithm to obtain the MLEs. Finally, some simulations are implemented in order to show the performance of the proposed method under finite samples and a case analysis is illustrated. [ABSTRACT FROM PUBLISHER]

Hepatitis B is a major global challenge, but there is a lack of epidemiological research on hepatitis B incidence from a change point perspective. This study aimed to fill this gap by identifying significant change points and trends in hepatitis time series in Xinjiang, China. The datasets were obtained from the Xinjiang Information System for Disease Control and Prevention. The Mann-Kendall-Sneyers (MKS) test was used to detect change points and trend changes on the hepatitis B time series of 14 regions in Xinjiang, and the effectiveness of this method was validated by comparing it with the binary segmentation (BS) and segment regression (SR) methods. Based on the results of change point analysis, the prevention and control policies and measures of hepatitis in Xinjiang were discussed. The results showed that 8 regions (57.1%) with at least one change fell within the 95% confidence interval (CI) in all 14 regions by the MKS test, where five regions (Turpan (TP), Hami (HM), Bayingolin (BG), Kyzylsu Kirgiz (KK), Altai (AT)) were identified at one change point, two change points existed for two regions (Aksu (AK), Hotan (HT)) and three change points was detected in 1 region (Bortala (BT)). Most of the change points occurred at both ends of the sequence. More change points indicated an upward trend in the front half of the sequence, while in the latter half, many change points indicated a downward trend prominently. Finally, in comparing the results of the three change point tests, the MKS test showed a 61.5% agreement (8/13) with the BS and SR.