A note on L1 consistent estimation
Journal
Canadian Journal of Statistics
Date Issued
January 1, 1988
Author(s)
DOI
10.2307/3314734
Abstract
Let (š³, š) be a space with a Ļāfield, M = {Ps; s o} a family of probability measures on A, Ī arbitrary, X1,ā¦,Xn independently and identically distributed P random variables. Metrize Ī with the L1 distance between measures, and assume identifiability. Minimumādistance estimators are constructed that relate rates of convergence with VapnikāCervonenkis exponents when M is āregularā. An alternative construction of estimates is offered via Kolmogorov's chain argument. Copyright Ā© 1988 Statistical Society of Canada