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2013 Inference for the mean of large $p$ small $n$ data: A finite-sample high-dimensional generalization of Hotelling’s theorem
Piercesare Secchi, Aymeric Stamm, Simone Vantini
Electron. J. Statist. 7: 2005-2031 (2013). DOI: 10.1214/13-EJS833

Abstract

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.

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Piercesare Secchi. Aymeric Stamm. Simone Vantini. "Inference for the mean of large $p$ small $n$ data: A finite-sample high-dimensional generalization of Hotelling’s theorem." Electron. J. Statist. 7 2005 - 2031, 2013. https://doi.org/10.1214/13-EJS833

Information

Published: 2013
First available in Project Euclid: 5 August 2013

zbMATH: 1293.62126
MathSciNet: MR3085016
Digital Object Identifier: 10.1214/13-EJS833

Subjects:
Primary: 62H10, 62H15

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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