  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.
