随机向量独立性检验的研究

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...

A Study on the Test of Independence of Random Vectors

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.