Cube root weak convergence of empirical estimators of a density level set
密度水平集经验估计量的立方根弱收敛
Given n independent random vectors with common density f on Rd, we study the weak convergence of three empirical-measure based estimators of the convex λ-level set Lλ of f, namely the excess mass set, the minimum volume set and the maximum probability set, all selected from a class of convex sets A that contains Lλ. Since these set-valued estimators approach Lλ, even the formulation of their weak convergence is nonstandard. We identify the joint limiting distribution of the…