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.
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.
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@article{CRMATH_2009__347_23-24_1429_0, author = {Aghoukeng Jiofack, Jean G\'erard and Nkiet, Guy Martial}, title = {Testing for equality of means of a {Hilbert} space valued random variable}, journal = {Comptes Rendus. Math\'ematique}, pages = {1429--1433}, publisher = {Elsevier}, volume = {347}, number = {23-24}, year = {2009}, doi = {10.1016/j.crma.2009.10.010}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.10.010/} }
TY - JOUR AU - Aghoukeng Jiofack, Jean Gérard AU - Nkiet, Guy Martial TI - Testing for equality of means of a Hilbert space valued random variable JO - Comptes Rendus. Mathématique PY - 2009 SP - 1429 EP - 1433 VL - 347 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.10.010/ DO - 10.1016/j.crma.2009.10.010 LA - en ID - CRMATH_2009__347_23-24_1429_0 ER -
%0 Journal Article %A Aghoukeng Jiofack, Jean Gérard %A Nkiet, Guy Martial %T Testing for equality of means of a Hilbert space valued random variable %J Comptes Rendus. Mathématique %D 2009 %P 1429-1433 %V 347 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.10.010/ %R 10.1016/j.crma.2009.10.010 %G en %F CRMATH_2009__347_23-24_1429_0
Aghoukeng Jiofack, Jean Gérard; Nkiet, Guy Martial. Testing for equality of means of a Hilbert space valued random variable. Comptes Rendus. Mathématique, Volume 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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