  In the context of density level set estimation, we study the convergence of
general plug-in methods under two main assumptions on the density for a given
level $\lambda$. More precisely, it is assumed that the density (i) is smooth
in a neighborhood of $\lambda$ and (ii) has $\gamma$-exponent at level
$\lambda$. Condition (i) ensures that the density can be estimated at a
standard nonparametric rate and condition (ii) is similar to Tsybakov's margin
assumption which is stated for the classification framework. Under these
assumptions, we derive optimal rates of convergence for plug-in estimators.
Explicit convergence rates are given for plug-in estimators based on kernel
density estimators when the underlying measure is the Lebesgue measure. Lower
bounds proving optimality of the rates in a minimax sense when the density is
H\"older smooth are also provided.
