Rates of Convergence of Minimum Distance Estimators and Kolmogorov's Entropy

Let (X, A) be a space with a -field, M = \Pₛ; s \ be a family of probability measures on A with arbitrary, X₁, , Xₙ i. i. d. observations on P_. Define ₙ (A) = (1/n) ⁿ₈ = ₁ IA (Xᵢ), the empirical measure indexed by A A. Assume is totally bounded when metrized by the L₁ distance between measures. Robust minimum distance estimators ₙ are constructed for and the resulting rate of convergence is shown naturally to depend on an entropy function for.