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基于似然比准则的稳健方差分析AI 解读

Robust tests of general linear hypotheses in linear models are developed. These are likelihood ratio type tests in the same sense that M -estimates are maximum likelihood type estimates. Construction of the tests suggests a decomposition of the data into terms analogous to classical sums of squares, providing a robust analysis of variance. Asymptotic efficiency and robustness properties of the tests are the same as those of the M -estimates upon which they are based.

条件渐近正态性的应用AI 解读

Summary Methods for obtaining the limiting distribution of a complicated statistic which depends on another auxiliary statistic are discussed. Examples are given in which a general conditional approach due to Sethuraman is found to be extremely fruitful in solving this type of problem.

基于一步 R 估计的一般线性模型稳健分析AI 解读

Classical analysis of variance with least squares fitting is often used to discern structure in a linear model. McKean & Hettmansperger (1976) proposed a robust analysis based on ranks using the R-estimates proposed by Jaeckel (1972). These rank procedures depend on minimizing a dispersion surface and as a result are computationally restricted to small to moderate sized sets. In this paper we propose one step iterations based on a second derivative approximation to the…

单样本位置问题的自适应稳健程序AI 解读

A family of rank statistics based on a set of simple scores functions is introduced. The distribution theory is briefly discussed, and both point and interval estimators for the center of an absolutely continuous symmetric distribution are presented. Given a random sample from a symmetric distribution, all subsequent inference is based on the member of the family of rank statistics having the smallest estimated asymptotic variance. The robustness properties are examined…

关于分布强收敛的一则札记AI 解读

If a sequence of distributions converges weakly to a distribution and if the associated densities are unimodal then the sequence of density functions converges to the density of the limiting distribution. This stronger form of convergence is useful in the investigation of limiting joint distributions.

针对有序备择的一类非参数同质性检验AI 解读

In this paper, the $c$-sample location problem with ordered or restricted alternatives is considered. Linear combinations of Chernoff-Savage type two-sample statistics computed among the $c(c - 1)/2$ pairs of samples are proposed as test statistics. It is shown that for each linear combination of two-sample statistics there is another linear combination, using only the $c - 1$ two-sample statistics based on adjacent samples as determined by the alternative, which has the…

尺度参数未知时的位置参数大样本保守检验AI 解读

Potthoff [6] has suggested a conservative test for location based on the Mann-Whitney statistic when the underlying distributions differ in shape. We propose a conservative test based on Mathisen's median statistic [5] and compare its properties to those of Potthoff's test.