SEMIPARAMETRICALLY EFFICIENT INFERENCE BASED ON SIGNED RANKS IN SYMMETRIC INDEPENDENT COMPONENT MODELS

• 成果类型: Article
• 署名作者: Ilmonen, Pauliina; Paindaveine, Davy
• 署名单位: Aalto University; Universite Libre de Bruxelles; Universite Libre de Bruxelles; Tampere University; Sorbonne Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS906
• 发表日期: 2011
• 页码: 2448-2476
• 关键词: Adaptive Estimation; shape

摘要

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 x 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 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.