多个正态总体均值相等的VDR检验

VDR test for equality of means of multiple normally distributed populations

本文将随机估计由一维参数扩展至多维参数,基于随机估计的密度函数提出VDR检验.在总体方差已知和未知的两种情形下,本文讨论多个正态总体均值是否相同的VDR检验过程,而且得到精确的检验.单因素方差分析是VDR检验的特例.模拟研究表明,VDR检验是一个普遍适用的方法.

This paper develops the concept on randomized estimation of one-dimensional parameter to that of vector parameter. The randomized estimator of vector parameter is de ned by using both pivotal quantity of the parameters and pivotal random vector. Based on test variable which is de ned through both randomized estimation and its probability density function, the VDR test is constructed. As an application, the proposed method is used to test whether the means of several normal distribution populations are equal or not. One-way analysis of variance is a special case of VDR test. The simulation study reveals that VDR test is a valid and uni ed approach. Some illustrations show that some classical results can be derived by VDR test.