Minimum L2 and robust Kullback-Leibler estimation

Abstract

This paper introduces two new robust methods for estimation of parameters in a given parametric family. The first method is that of `minimum weighted L2', effectively minimising an estimate of the integrated (and possibly weighted) squared error. The second is `robust Kullback-Leibler', consisting of minimising a robust version of the empirical Kullback-Leibler distance, and can be viewed as a general robust modification of the maximum likelihood procedure. This second method is also related to recent local likelihood ideas for semiparametric density estimation. The methods are described, influence functions are found, as are formulae for asymptotic variances. In particular large-sample efficiencies are computed under the home turf conditions of the underlying parametric model. The methods and formulae are illustrated for the normal model.

arXiv comment4 pages, 0 figure. This arXiv'd February 2026 paper is from the 12th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes proceedings volume, 1994, pages 102-105. The material preshadows local likelihood and BHHJ estimation