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Semiparametrically efficient inference based on signed ranks in symmetric independent component models

par Ilmonen, Sirkku Pauliina ;Paindaveine, Davy
Référence Annals of statistics, 39, page (2448-2476)
Publication Publié, 2011

Article révisé par les pairs

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Résumé :

We consider semiparametric location-scatter models for which the p-variate observation is obtained as X=Lambda Z+mu, where mu is a p-vector, Lambda is a full-rank p*p matrix, and the (unobserved) random p-vector Z has marginals that are centered and mutually independent but are otherwise unspecified. As in blind source separation and independent component analysis (ICA), the parameter of interest throughout the paper is Lambda. On the basis of n i.i.d. copies of X, we develop, under a symmetry assumption on Z, signed-rank one-sample testing and estimation procedures for Lambda. We exploit the uniform local and asymptotic normality (ULAN) of the model to define signed-rank procedures that are semiparametrically efficient under correctly specified densities. Yet, as usual in rank-based inference, the proposed procedures remain valid (correct asymptotic size under the null, for hypothesis testing, and root-n consistency, for point estimation) under a very broad range of densities. We derive the asymptotic properties of the proposed procedures and investigate their finite-sample behavior through simulations.