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Journal Articles Electronic Journal of Statistics Year : 2013

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

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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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Dates and versions

inserm-00858214 , version 1 (04-09-2013)

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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 , 2013, 7, pp.2005-31. ⟨10.1214/13-EJS833⟩. ⟨inserm-00858214⟩
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