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

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

2012-02-23

arxiv.org/abs/1202.5159v1

Annals of Statistics 2011, Vol. 39, No. 5, 2448-2476

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS906 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/11-AOS906

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 $p\times p$ 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.

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