位置与刻度参数变点的非参数检验及其渐近性质

若X1,…,Xr,Xr＋1,…,Xn是一列独立的随机变量,且X1,…,Xr iid.～F（x）,Xr＋1,…,Xn iid.～F（x-u/σ）,其中F（x）为连续分布函数,u,σ为未知参数,分别称为位置参数和刻度参数,r（1＜r＜n）或r/n（记为t0）称为序列的变点.运用次序统计量构造了U-统计量,并且基于U-统计量,讨论了位置与刻度参数模型的变点检验问题,并证明了检验统计量的渐近正态性.     

A New Class of Distribution-Free Tests for Location Parameters

Abstract

A new class of distribution-free tests for the two-sample location problem is proposed. The tests are based on two-sample U-statistics. This class basically generalizes the tests proposed by Deshpande, J.V.; Kochar, S.C. Some competitors of Wilcoxon–Mann–Whitney test for location alternatives. Journal of Indian Statistical Association 1982, 19, 9–18. The proposed class of tests is also extended to the k (≥ 2)-sample problem for testing homogeneity of location parameters against ordered alternatives. This extension is based on linear combinations of two-sample U-statistics. Pitman asymptotic relative efficiencies (AREs) of the members of the proposed class(es) of tests relative to some of the existing tests are computed for a number of underlying distributions. It is shown that the proposed class of tests performs as good as or better than its competitors in literature.