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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 onreplacing the unknown density by some nonparametric estimator, usually thekernel. Thus, the bandwidth selection is a fundamental problem from a practicalpoint of view. Recently, specific selectors for level sets have been proposed.However, if some a priori information about the geometry of the level set isavailable, then excess mass algorithms can be useful. In this case, a densityestimator is not necessary, and the problem of bandwidth selection can beavoided. The third methodology is a hybrid of the others. As in the excess massmethod, it assumes a mild geometric restriction on the level set and, like theplug-in approach, requires a pilot nonparametric estimator of the density. Oneinteresting open question concerns the practical performance of these methods.In this work, existing methods are reviewed, and two new hybrid algorithms areproposed. Their practical behaviour is compared through extensive simulations.

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