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Comptes Rendus Mathématique
Volume 347, n° 23-24
pages 1429-1433 (décembre 2009)
Doi : 10.1016/j.crma.2009.10.010
Received : 10 May 2009 ;  accepted : 23 September 2009
Testing for equality of means of a Hilbert space valued random variable
Un test d’égalité des moyennes d’une variable aléatoire à valeurs dans un espace de Hilbert
 

Jean Gérard Aghoukeng Jiofack a, b , Guy Martial Nkiet a
a Université des sciences et techniques de Masuku, URMI, BP 943, Franceville, Gabon 
b Université de Yaoundé 1, faculté des sciences, département de mathématiques, BP 812, Yaoundé, Cameroun 

Abstract

We propose a test for equality of means of a random variable valued into a real separable Hilbert space. The test statistic is based on projections of empirical means onto spaces spanned by principal directions obtained from principal component analysis of the random variable. The asymptotic distribution of this test statistic is derived under the null hypothesis and the consistency of the obtained test is proved. An application to the case of functional variables is indicated. To cite this article: J.G. Aghoukeng Jiofack, G.M. Nkiet, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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Résumé

Nous proposons un test d’égalité des moyennes pour une variable aléatoire à valeurs dans un espace de Hilbert réel séparable. La statistique de test est basée sur des projections des moyennes empiriques sur des directions obtenues à partir de l’analyse en composantes principale de la variable aléatoire. La loi limite, sous hypothèse nulle, de cette statistique de test est obtenue et la convergence du test obtenu est prouvée. L’application au cas de variables fonctionnelles est indiquée. Pour citer cet article : J.G. Aghoukeng Jiofack, G.M. Nkiet, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.


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