no. 23-24
Statistics/Probability Theory
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]

Présenté par : Paul Deheuvels

Aghoukeng Jiofack, Jean Gérard1, 2 ; Nkiet, Guy Martial1
1 Université des sciences et techniques de Masuku, URMI, BP 943, Franceville, Gabon
2 Université de Yaoundé 1, faculté des sciences, département de mathématiques, BP 812, Yaoundé, Cameroun
Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1429-1433.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.10.010
Aghoukeng Jiofack, Jean Gérard 1, 2 ; Nkiet, Guy Martial 1

1 Université des sciences et techniques de Masuku, URMI, BP 943, Franceville, Gabon
2 Université de Yaoundé 1, faculté des sciences, département de mathématiques, BP 812, Yaoundé, Cameroun 
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Aghoukeng Jiofack, Jean Gérard; Nkiet, Guy Martial. Testing for equality of means of a Hilbert space valued random variable. Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1429-1433. doi : 10.1016/j.crma.2009.10.010. http://www.numdam.org/articles/10.1016/j.crma.2009.10.010/

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