随机向量独立性检验的研究  

A Study on the Test of Independence of Random Vectors

作　　者：徐文青[1] 

机构地区：[1]河南工程学院数理科学系,河南郑州451191

出　　处：《河南工程学院学报（自然科学版）》2011年第3期64-67,共4页Journal of Henan University of Engineering：Natural Science Edition

基　　金：河南工程学院青年基金(Y2010019)

摘　　要：现有的二维随机向量(X,Y)独立性检验方法都以假设X和Y相互独立为原假设进行检验,具有保护原假设的倾向,即更容易得到接受"两个变量相互独立"的结论.在"两个变量不相互独立"为原假设的基础上,利用分布函数的Kolmogorov距离构建了一种检验方法,使得能够控制将"X和Y不独立"错判成"X和Y相互独立"的概率.数据模拟表明,该方法能更好地区分不独立的随机变量.This thesis discusses the methods about the test of independence of two - dimensional random vectors （ X, Y ）. The traditional test methods are based on the null hypothesis that X and Y are independent . We know that the hypothesis test has a tendency of protection of the null hypothesis, that is to say, it＇s easier to accept that ＂two variables are independent ＂ . In this thesis, we utilize the Kolmogorov distance of distribution functions to construct a new test method based on the null hypothesis that X and Y are not independent. This method allows us to control the probability of the wrong judgment that ＂X and Y are independent＂ , when ＂X and Y are not independent＂ is right. Data simulation shows that the new method can better distinguish random variables which are not independent.

关 键 词：独立性检验 Pearson统计量 Spearman统计量 均匀分布 Kolmogorov距离 

分 类 号：O212.1[理学—概率论与数理统计]