  We investigate the estimation of a weighted density taking the form
$g=w(F)f$, where $f$ denotes an unknown density, $F$ the associated
distribution function and $w$ is a known (non-negative) weight. Such a class
encompasses many examples, including those arising in order statistics or when
$g$ is related to the maximum or the minimum of $N$ (random or fixed)
independent and identically distributed (\iid) random variables. We here
construct a new adaptive non-parametric estimator for $g$ based on a plug-in
approach and the wavelets methodology. For a wide class of models, we prove
that it attains fast rates of convergence under the $\mathbb{L}_p$ risk with
$p\ge 1$ (not only for $p = 2$ corresponding to the mean integrated squared
error) over Besov balls. The theoretical findings are illustrated through
several simulations.
