Inference for the Mean of Large p Small n Data: a Finite-Sample High-Dimensional Generalization of Hotelling's Theorem

Piercesare Secchi 1, * Aymeric Stamm 2, * Simone Vantini 1, *
* Corresponding author
2 VisAGeS - Vision, Action et Gestion d'informations en Santé
INSERM - Institut National de la Santé et de la Recherche Médicale : U746, Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : We provide a generalization of Hotelling's Theorem that en- ables 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 par- ticular, we extend some recent results presented in the literature by finding the (finite-n) p-asymptotic distribution of the Generalized Hotelling's T2 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. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2013, 7, pp.2005-31. ⟨10.1214/13-EJS833⟩. ⟨inserm-00858214⟩

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