Testing for equality of means of a Hilbert space valued random variable

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).