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Mathematics Analysis Seminar: Hausdorff Estimation of Density Level Sets
4:10pm, Neill 5W
In this talk, we will discuss the Hausdorff estimation of sup level sets of a density function f based on n independent observations X_1, X_2, ... ,X_n from the density. First, we will discuss the error measure using Hausdorff distance and then make some assumptions for the density in order to get a better result. The estimation will be divided into two parts, one when regularity is known and the other for when regularity is unknown. In both cases, we will provide an upper bound on the Hausdorff error which converges to zero as n goes to infinity.