  We consider a multivariate density model where we estimate the excess mass of
the unknown probability density $f$ at a given level $\nu>0$ from $n$ i.i.d.
observed random variables. This problem has several applications such as
multimodality testing, density contour clustering, anomaly detection,
classification and so on. For the first time in the literature we estimate the
excess mass as an integrated functional of the unknown density $f$. We suggest
an estimator and evaluate its rate of convergence, when $f$ belongs to general
Besov smoothness classes, for several risk measures. A particular care is
devoted to implementation and numerical study of the studied procedure. It
appears that our procedure improves the plug-in estimator of the excess mass.
