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October 2011 Semiparametrically efficient inference based on signed ranks in symmetric independent component models
Pauliina Ilmonen, Davy Paindaveine
Ann. Statist. 39(5): 2448-2476 (October 2011). DOI: 10.1214/11-AOS906

Abstract

We consider semiparametric location-scatter models for which the p-variate observation is obtained as X = ΛZ + μ, where μ is a p-vector, Λ 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 Λ. 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 Λ. 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 is 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.

Citation

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Pauliina Ilmonen. Davy Paindaveine. "Semiparametrically efficient inference based on signed ranks in symmetric independent component models." Ann. Statist. 39 (5) 2448 - 2476, October 2011. https://doi.org/10.1214/11-AOS906

Information

Published: October 2011
First available in Project Euclid: 30 November 2011

zbMATH: 1231.62043
MathSciNet: MR2906874
Digital Object Identifier: 10.1214/11-AOS906

Subjects:
Primary: 62G05, 62G10
Secondary: 62G20, 62H99

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 5 • October 2011
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