Inference under Heteroscedasticity of Unknown Form Using an Adaptive Estimator

The heteroscedasticity consistent covariance matrix estimators are commonly used for the testing of regression coefficients when error terms of regression model are heteroscedastic. These estimators are based on the residuals obtained from the method of ordinary least squares and this method yields inefficient estimators in the presence of heteroscedasticity. It is usual practice to use estimated weighted least squares method or some adaptive methods to find efficient estimates of the regression parameters when the form of heteroscedasticity is unknown. But HCCM estimators are seldom derived from such efficient estimators for testing purposes in the available literature. The current article addresses the same concern and presents the weighted versions of HCCM estimators. Our numerical work uncovers the performance of these estimators and their finite sample properties in terms of interval estimation and null rejection rate.     

Probabilistic Properties of Parametric Dual and Inverse Time Series Models Generated by ARMA Models

For the class of autoregressive-moving average (ARMA) processes, we examine the relationship between the dual and the inverse processes. It is demonstrated that the inverse process generated by a causal and invertible ARMA (p, q) process is a causal and invertible ARMA (q, p) model. Moreover, it is established that this representation is strong if and only if the generating process is Gaussian. More precisely, it is derived that the linear innovation process of the inverse process is an all-pass model. Some examples and applications to time reversibility are given to illustrate the obtained results.     

Stabilizing the Performance of Kurtosis Estimator of Multivariate Data

The estimation of the kurtosis parameter of the underlying distribution plays a central role in many statistical applications. The central theme of the article is to improve the estimation of the kurtosis parameter using a priori information. More specifically, we consider the problem of estimating kurtosis parameter of a multivariate population when some prior information regarding the the parameter is available. The rationale is that the sample estimator of the kurtosis parameter has a large estimation error. In this situation we consider shrinkage and pretest estimation methodologies and reappraise their statistical properties. The estimation based on these strategies yield relatively smaller estimation error in comparison with the sample estimator in the candidate subspace. A large sample theory of the suggested estimators are developed and compared. The results demonstrate that suggested estimators outperform the estimator based on the sample data only in the candidate subspace. In an effort to appreciate the relative behavior of the estimators in a finite sample scenario, a Monte-carlo simulation study is planned and performed. The result of simulation study strongly corroborates the asymptotic result. To illustrate the application of the estimators, some example are showcased based on recently published data.     

纪念苏丹商人穆罕默德·哈吉在华首设商务处

中国与阿拉伯非洲的历史交往源远流长,特别是与苏丹的联系,可以追溯到西汉时期,而且从那时起双方之间的往来一直延续不断.本文在历史回顾的基础上,通过实地调查和口传资料,着重考察了19世纪末苏丹商人穆罕默德·哈吉在广州首设商务办事处并开展苏(丹)中(国)贸易、加强双方社会联系的历史活动,揭示了苏中悠久关系史上鲜为人知的一页.     

伊斯兰与恐怖主义行为

(一) 2005年7月7日和7月21日,伦敦相继发生恐怖主义爆炸事件;2005年7月23日埃及沙姆沙伊赫也发生了恐怖主义袭击事件,这些事件引发了许多亟待解决的问题.     

Support vector regression based residual control charts

Control charts for residuals, based on the regression model, require a robust fitting technique for minimizing the error resulting from the fitted model. However, in the multivariate case, when the number of variables is high and data become complex, traditional fitting techniques, such as ordinary least squares (OLS), lose efficiency. In this paper, support vector regression (SVR) is used to construct robust control charts for residuals, called SVR-chart. This choice is based on the fact that the SVR is designed to minimize the structural error whereas other techniques minimize the empirical error. An application shows that SVR methods gives competitive results in comparison with the OLS and the partial least squares method, in terms of standard deviation of the error prediction and the standard error of performance. A sensitivity study is conducted to evaluate the SVR-chart performance based on the average run length (ARL) and showed that the SVR-chart has the best ARL behaviour in comparison with the other residuals control charts.     

Behaviour of skewness, kurtosis and normality tests in long memory data

We establish the limiting distributions for empirical estimators of the coefficient of skewness, kurtosis, and the Jarque–Bera normality test statistic for long memory linear processes. We show that these estimators, contrary to the case of short memory, are neither ${\sqrt{n}}We establish the limiting distributions for empirical estimators of the coefficient of skewness, kurtosis, and the Jarque–Bera normality test statistic for long memory linear processes. We show that these estimators, contrary to the case of short memory, are neither ?n{\sqrt{n}}-consistent nor asymptotically normal. The normalizations needed to obtain the limiting distributions depend on the long memory parameter d. A direct consequence is that if data are long memory then testing normality with the Jarque–Bera test by using the chi-squared critical values is not valid. Therefore, statistical inference based on skewness, kurtosis, and the Jarque–Bera normality test, needs a rescaling of the corresponding statistics and computing new critical values of their nonstandard limiting distributions.     

Test of symmetry based on copula function

We introduce some new nonparametric statistical tests of symmetry. The limiting behaviors of the proposed statistics are established under the null hypothesis. Emphasis is placed on explanation of the strong approximation methodology. The asymptotic validity of a re-sampling method to compute p-values is also established. A simulation study for some considered statistics is performed.