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A generalization of Hotelling's theorem for large p small n data

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 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. We find suitable test statistics and their p-asymptotic distributions that allow the inferential analysis of large p small n data (e.g., spectral data, micro-arrays, and functional data). The convergence rate of the new statistic to its p-asymptotic distribution is analyzed by means of MC simulations, as well as its power which is compared with that of two recent alternatives: a model-dependent test relying on stronger assumptions (Srivastava (2007)) and a model-free permutation test relying on weaker assumptions (Pesarin and Salmaso (2010)).
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Submitted on : Wednesday, September 4, 2013 - 8:56:38 PM
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  • HAL Id : inserm-00858212, version 1


Piercesare Secchi, Aymeric Stamm, Simone Vantini. A generalization of Hotelling's theorem for large p small n data. Statistical Computation and Complex Systems, Sep 2011, Italy. pp.0-0. ⟨inserm-00858212⟩



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