Additive Estimates and Data Splitting

Abstract

Assume that we are given a class of density estimates parametrized by θ ∈ Θ, such that f _{n, θ} denotes the density estimate with parameter θ. Our goal is to construct a density estimate f _n whose L ₁ error is (almost) as small as that of the best estimate among the f _n,θ , θ ∈ Θ. Applying the minimum distance estimate of Chapter 5 directly to this class is often problematic because of the dependence of each estimate in the class and the empirical measure μ _n .