A generalization of Hotelling's theorem for large p small n data
Résumé
We provide a generalization of Hotelling's Theorem that enables inference (i) for the mean vector of a multivariate normal population and (ii) for the comparison of the mean vectors of two multivariate normal populations, when the number p of components is larger than the number n of sample units and the (common) covariance matrix is unknown. We find suitable test statistics and their p-asymptotic distributions that allow the inferential analysis of large p small n data (e.g., spectral data, micro-arrays, and functional data). The convergence rate of the new statistic to its p-asymptotic distribution is analyzed by means of MC simulations, as well as its power which is compared with that of two recent alternatives: a model-dependent test relying on stronger assumptions (Srivastava (2007)) and a model-free permutation test relying on weaker assumptions (Pesarin and Salmaso (2010)).
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Secchi_Stamm_Vantini_-_2011_-_A_generalization_of_Hotelling_s_theorem_for_large_p_small_n_data.pdf (92.22 Ko)
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