A comparative simulation study of data-driven methods for estimating density level sets

Density level sets are mainly estimated using one of three methodologies: plug-in, excess mass, or a hybrid approach. The plug-in methods are based on replacing the unknown density by some nonparametric estimator, usually the kernel one. Thus, the bandwidth selection is a fundamental problem from an applied perspective. Recently, specific selectors for level sets have been proposed. However, if some a priori information about the geometry of the level set is available, then excess mass algorithms can be useful. In this case, the problem of bandwidth selection can be avoided. The third methodology is a hybrid of the others. It assumes a mild geometric restriction on the level set and it requires a pilot nonparametric estimator of the density. One interesting open question concerns the performance of these methods. In this work, existing methods are reviewed, and two new hybrid algorithms are proposed. Their practical behaviour is compared through extensive simulation study.