序约束下多元正态均值的检验问题

TESTS FOR HOMOGENEITY OF CONSTRAINED MULTIVARIATE NORMAL MEAN VECTORS

设有k组均值有简单半序约束,协方差阵未知的p维正态分布．Sasabuchi等在2003年研究了均值是否相等的检验问题．考虑到似然比检验统计量的临界点难以获得,以致于它不容易实施,Sasabuchi提出了一个检验方法．称为Sasabuchi检验．Sasabuchi检验的一个不足之处在于,它并不优于经典的MANOVA检验．作者提出了一个新的检验方法,它比Sasabuchi检验有一致优的势,而且形式更为简单．通过模拟发现这个检验方法还优势于MANOVA．最后导出了这个检验统计量的渐近零分布．

Suppose that simple-order restriction is imposed among several p-variate nor- mal mean vectors, which has unknown common covariance matrix. By noting the difficulty in obtaining the critical points of liklihood ratio test, Sasabuchi et al.＇s （2003）（[1]） proposed an alternative test statistic （Sasabuchi Test） for testing the homogeneity of these mean vectors under simple-order restriction. Sasabuchi Test does not compare favorably with MANOVA. In this paper, a new test statistic which is uniformly more powerful than Sasabuchi Test is given, it is also found that our test are more powerful than MANOVA by simulation, and the asymptotic distribution of this test statistic under the null hypothesis is derived.