On the asymptotic normality of the R-estimators of the slope parameters of simple linear regression models with associated errors

ABSTRACT

The purpose of this paper is to prove, under mild conditions, the asymptotic normality of the rank estimator of the slope parameter of a simple linear regression model with stationary associated errors. This result follows from a uniform linearity property for linear rank statistics that we establish under general conditions on the dependence of the errors. We prove also a tightness criterion for weighted empirical process constructed from associated triangular arrays. This criterion is needed for the proofs which are based on that of Koul [Behavior of robust estimators in the regression model with dependent errors. Ann Stat. 1977;5(4):681–699] and of Louhichi [Louhichi S. Weak convergence for empirical processes of associated sequences. Ann Inst Henri Poincaré Probabilités Statist. 2000;36(5):547–567].     

Asymptotic behaviour of proportions of observations in random regions determined by central order statistics from stationary processes

In this paper, we show that proportions of observations that fall into a random region determined by a given Borel set and a central order statistic converge almost surely, provided that the corresponding population quantile is unique. We also describe three types of possible asymptotic behaviour of these proportions in the case of non-unique population quantile. As an application of our findings we establish limiting properties of numbers of ties with a central order statistics in a discrete sample. Our results are derived not only for independent and identically distributed observations but more generally for strictly stationary and ergodic sequences of random variables.     

Multiple comparisons in two-factor testing of psychophysical thresholds by the delta test method

We propose an algorithm of multiple comparisons in two-factor testing of psychophysical thresholds. We use logistic regression combined with guessing rate and adopt the step-down procedure with Ryan–Einot–Gabriel–Welsch (REGW) significance levels for multiple test. We test hypotheses of main effects and interaction in two-factor problem by using the delta test statistics.     

Bayesian prediction of order statistics with fixed and random sample sizes based on k-record values from Pareto distribution

In this paper, the two-parameter Pareto distribution is considered and the problem of prediction of order statistics from a future sample and that of its geometric mean are discussed. The Bayesian approach is applied to construct predictors based on observed k-record values for the cases when the future sample size is fixed and when it is random. Several Bayesian prediction intervals are derived. Finally, the results of a simulation study and a numerical example are presented for illustrating all the inferential procedures developed here.     

Comparison of preliminary test estimators based on generalized order statistics from proportional hazard family using Pitman measure of closeness

In this article, based on generalized order statistics from a family of proportional hazard rate model, we use a statistical test to generate a class of preliminary test estimators and shrinkage preliminary test estimators for the proportionality parameter. These estimators are compared under Pitman measure of closeness (PMC) as well as MSE criteria. Although the PMC suffers from non transitivity, in the first class of estimators, it has the transitivity property and we obtain the Pitman-closest estimator. Analytical and graphical methods are used to show the range of parameter in which preliminary test and shrinkage preliminary test estimators perform better than their competitor estimators. Results reveal that when the prior information is not too far from its real value, the proposed estimators are superior based on both mentioned criteria.     

Theory and methods for partitioned Gini coefficients computed on post-stratified data

The Gini coefficient is used to measure inequality in populations. However, shifts in the population distribution may affect subgroups differently. Consequently, it can be informative to examine inequality separately for these segments. Consider an independently and identically distributed sample split based on ranking and compute the Gini coefficient for each partition. These coefficients, calculated from post-stratified data, are not functions of U-statistics. Therefore, previous theoretical and methodological results cannot be applied. In this article, the asymptotic joint distribution is derived for the partitioned coefficients and bootstrap methods for inference are developed. Finally, an application to per capita income across census tracts is examined.     

Progressively Type-II censored conditionally N-ordered statistics from a unified elliptically contoured copula

Progressively Type-II censored conditionally N-ordered statistics (PCCOS-N) arising from iid random vectors X_i = (X¹_i, X²_i, …, X_i^p), i = 1, 2…, n, were investigated by Bairamov (2006 Bairamov, I. (2006). Progressive Type II censored order statistics for multivariate observations. J. Mult. Anal. 97:797–809.[Crossref], [Web of Science ®] , [Google Scholar]), with respect to the magnitudes of N(X_i), i = 1, 2, …, n, where N( · ) is a p-variate measurable function defined on the support set of X₁ satisfying certain regularity conditions and N(X_i) denotes the lifetime of the random vector X_i, i = 1, …, n. Under the PCCOS-N sampling scheme, n independent units are placed on a life-test and after the ith failure, R_i (i = 1, …, m) of the surviving units are removed at random from the remaining observations. In this article, we consider PCCOS-N arising from a vector with identical as well as non identical dependent components, jointly distributed according to a unified elliptically contoured copula (PCCOSDUECC-N). Results established here contain the previous results as particular cases. Illustrative examples and simulation studies show that PCCOSDUECC-N enables us to analyze the lifetime of several systems, including repairable systems and systems with standby components, more efficiently than PCCOS-N.     

对高校双语教学的思考和认识

双语教学已经成为我国课程教学的发展趋势,开展双语教学是培养具有国际合作意识、国际交流能力和具有国际竞争力的外向型人才的客观要求。文章对数理统计双语教学的必要性以及在双语教学的实践中应该注意的问题进行了探讨,并提出了解决问题的方法。     

关于高校就业率的思考

高校就业率政策在激发高校提高办学质量、重视就业指导工作等方面起着积极的作用。随着我国教育体制改革的深入,高等教育由精英化向大众化转变,大学生就业问题逐渐成为社会关注焦点之一,高校毕业生就业率也日益受到重视。针对目前就业率评价与统计过程中出现的问题,提出理性地看待高校就业率就要合理设置统计时间、科学界定就业率统计途径、结合就业率与就业质量来评价高校就业情况。     

Exact permutation inference for two sample repeated measures data

Experiments in which very few units are measured many times sometimes present particular difficulties. Interest often centers on simple location shifts between two treatment groups, but appropriate modeling of the error distribution can be challenging. For example, normality may be difficult to verify, or a single transformation stabilizing variance or improving normality for all units and all measurements may not exist. We propose an analysis of two sample repeated measures data based on the permutation distribution of units. This provides a distribution free alternative to standard analyses. The analysis includes testing, estimation and confidence intervals. By assuming a certain structure in the location shift model, the dimension of the problem is reduced by analyzing linear combinations of the marginal statistics. Recently proposed algorithms for computation of two sample permutation distributions, require only a few seconds for experiments having as many as 100 units and any number of repeated measures. The test has high asymptotic efficiency and good power with respect to tests based on the normal distribution. Since the computational burden is minimal, approximation of the permutation distribution is unnecessary.