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We consider semiparametric location-scatter models for which the $p$-variateobservation 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 areotherwise unspecified. As in blind source separation and independent componentanalysis (ICA), the parameter of interest throughout the paper is $\Lambda$. Onthe basis of $n$ i.i.d. copies of $X$, we develop, under a symmetry assumptionon $Z$, signed-rank one-sample testing and estimation procedures for $\Lambda$.We exploit the uniform local and asymptotic normality (ULAN) of the model todefine signed-rank procedures that are semiparametrically efficient undercorrectly specified densities. Yet, as is usual in rank-based inference, theproposed procedures remain valid (correct asymptotic size under the null, forhypothesis testing, and root-$n$ consistency, for point estimation) under avery broad range of densities. We derive the asymptotic properties of theproposed procedures and investigate their finite-sample behavior throughsimulations.

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