Large p Small n: Inference for the Mean

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 present a new result that enables inference for the mean vector of a multivariate normal random variable when the number p of its components is far larger than the number n of sample units and the covariance structure is completely unknown. The result turns out to be a useful tool for the inferential analysis (e.i. confidence region and hypothesis testing) of data up to now mostly studied only within an explorative perspective, like functional data. To this purpose, an application to the analysis of brain vascular vessel geometry is developed and shown.
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Piercesare Secchi, Aymeric Stamm, Simone Vantini. Large p Small n: Inference for the Mean. 45th Scientific Meeting of the Italian Statistical Society (SIS), Jun 2010, Padua, Italy. ⟨inria-00540565⟩

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