文章基本信息

标题：Inference for the mean of large $p$ small $n$ data: A finite-sample high-dimensional generalization of Hotelling’s theorem
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作者：Piercesare Secchi ; Aymeric Stamm ; Simone Vantini 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：2005-2031
DOI：10.1214/13-EJS833
语种：English
出版社：Institute of Mathematical Statistics
摘要：We provide a generalization of Hotelling’s Theorem that enables inference (i) for the mean vector of a multivariate normal population and (ii) for the comparison of the mean vectors of two multivariate normal populations, when the number $p$ of components is larger than the number $n$ of sample units and the (common) covariance matrix is unknown. In particular, we extend some recent results presented in the literature by finding the (finite-$n$) $p$-asymptotic distribution of the Generalized Hotelling’s $T^{2}$ enabling the inferential analysis of large-$p$ small-$n$ normal data sets under mild assumptions.