A useful approach to identify the multicollinearity in the presence of outliers

The presence of outliers in the data sets affects the structure of multicollinearity which arises from a high degree of correlation between explanatory variables in a linear regression analysis. This affect could be seen as an increase or decrease in the diagnostics used to determine multicollinearity. Thus, the cases of outliers reduce the reliability of diagnostics such as variance inflation factors, condition numbers and variance decomposition proportions. In this study, we propose to use a robust estimation of the correlation matrix obtained by the minimum covariance determinant method to determine the diagnostics of multicollinearity in the presence of outliers. As a result, the present paper demonstrates that the diagnostics of multicollinearity obtained by the robust estimation of the correlation matrix are more reliable in the presence of outliers.     

Data Dependent Cells Chi‐Square Test With Recurrent Events

We consider a recurrent event wherein the inter‐event times are independent and identically distributed with a common absolutely continuous distribution function F. In this article, interest is in the problem of testing the null hypothesis that F belongs to some parametric family where the q‐dimensional parameter is unknown. We propose a general Chi‐squared test in which cell boundaries are data dependent. An estimator of the parameter obtained by minimizing a quadratic form resulting from a properly scaled vector of differences between Observed and Expected frequencies is used to construct the test. This estimator is known as the minimum chi‐square estimator. Large sample properties of the proposed test statistic are established using empirical processes tools. A simulation study is conducted to assess the performance of the test under parameter misspecification, and our procedures are applied to a fleet of Boeing 720 jet planes' air conditioning system failures.     

正确理解我国现阶段按生产要素分配问题

当前,我国农村普遍建立了居民最低生活保障制度,这是保障农村社会稳定的"最后一道安全网",是中国农村社会保障体系的基础工程.但是,我国农村居民最低生活保障制度也还存在一些问题,例如保障对象、保障方式、保障资金、管理体制等,充分认识并采取有效措施解决好这些问题,对于完善农村社会保障体系,维护农村社会稳定和经济发展有着重要现实意义.     

关于最低生活保障城乡一体化研究——以安徽省为例

目前,我国社会保障制度改革进入一个新的重要时期。围绕如何实现经济社会的全面协调可持续发展,安徽省已经开始在部分地区进行了社会救助管理城乡一体化实践。在取得了一定的积极成果的同时,也发现了漏洞和不足,尤其是城乡低保制度的失衡问题突出。进一步完善社会救助体系,推进城乡低保一体化建设,要结合区域特点,因地制宜,分阶段分步骤,逐步实现。要在探索建立城乡低保一体化架构、完善运行机制、加强过程控制、加强财政保障机制建设、城乡低保队伍建设等方面,进行改进和完善,进行全面系统的顶层设计和思考。     

Estimators of percentiles based on absolute loss

Estimators of percentiles of location and scale parameter distributions are optimized based on Pitman closeness and absolute risk. A median unbiased (MU) estimator and a minimum risk (MR) estimator are shown to exist within a class of estimators, and to depend upon the medians of two completely specified distributions.     

A generalized improvement procedure for variance bounds for minimum variance unbiased estimator in inverse sampling

New bounds are obtained for the variance of the minimum variance unbiased estimator of p i n inverse sampling. A generalized procedure for further improving the bounds is also discussed.     

略论限度观

限度对于人们生存和发展具有重要的指导意义。为更好地适应时代发展要求，人们应该确立科学合理的限度观：必须恪守“最低限度”，应该追求“最大限度”，务必防止“无意过度”，可以倡导“超越限度”。确立科学合理限度观体现了科学发展的精神，有利于和谐社会的构建，有益于社会主客体的发展。人们要在实践和感悟中去寻求、把握和发展限度。科学合理限度观的确立，必须坚持求真务实、持续发展和公正发展等实践原则。     

Equality of two blues and ridge-type estimates

Equality is shown of the g-inverse and Moore-Penrose inverse representation of the BLUE in the general linear model. The proof is based on a matrix identity which allows also to establish a functional relationship between the BLUE and Ridge-type estimates.     

数论函数f(n)=n+[k/n]的最小值和最小值点

以[x]表不小于x的最小整数,设函数f(n)=n+[k/n],其中k为给定正整数,自变量n在正整数集取值。本文指出函数f(n)在整个定义域上的最小值和全部最小值点。     

PREDICTION OF THE FINITE POPULATION DISTRIBUTION FUNCTION UNDER GAUSSIAN SUPERPOPULATION MODELS

This article considers optimal prediction of the finite population distribution function under Gaussian superpopulation models, which allows auxiliary prior information to be incorporated into the estimation process. Large sample approximations for the variance of the optimal predictors are derived in some special important cases. A small scale Monte Carlo study illustrates comparisons between the optimal predictor and some others which are proposed in the literature. The conclusion is that the optimal predictor can be considerably more efficient in situations where the normal superpopulation model is adequate.