A test for the mean vector with fewer observations than the dimension under non-normality
A test for the mean vector with fewer observations than the dimension under non-normality
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DOI：
10.1016/j.jmva.2008.06.006
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发表时间：
2009-03
期刊：
影响因子：
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通讯作者：
M. Srivastava
中科院分区：
文献类型：
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作者：
M. Srivastava
本文考虑了模型xj=μ+Czj，j= 1，.，N中均值向量μ=0的检验问题，其中zj为随机p-向量，[式：见正文]和zij独立同分布，具有有限四阶矩，i= 1，.，p，j = 1，.，N，即不需要服从正态分布.我们假设C是一个p×p非奇异矩阵，并且观测值少于维数N≤p。我们考虑检验统计量，其中x <$是样本均值向量，S=（sij）是样本协方差矩阵，DS= diag（s11，.，spp），R=Ds− 12 SDs − 12，n=N−1。导出了检验统计量T的渐近零分布和非零分布。
In this article, we consider the problem of testing that the mean vector μ=0 in the model xj=μ+Czj,j=1,…,N, where zjare random p-vectors, [Formula: see text] and zijare independently and identically distributed with finite four moments, i=1,…,p,j=1,…,N; that is xineed not be normally distributed. We shall assume that C is a p×p non-singular matrix, and there are fewer observations than the dimension, N≤p. We consider the test statistic where x¯ is the sample mean vector, S=(sij) is the sample covariance matrix, DS= diag (s11,…,spp),R=Ds−12SDs−12and n=N−1. The asymptotic null and non-null distributions of the test statistic T are derived.