A note on L<inf>1</inf> consistent estimation

Abstract

Let (𝒳, 𝒜) be a space with a σ‐field, M = {Ps; s o} a family of probability measures on A, Θ arbitrary, X1,…,Xn independently and identically distributed P random variables. Metrize Θ with the L1 distance between measures, and assume identifiability. Minimum‐distance estimators are constructed that relate rates of convergence with Vapnik‐Cervonenkis exponents when M is “regular”. An alternative construction of estimates is offered via Kolmogorov's chain argument. Copyright © 1988 Statistical Society of Canada