Weighted sampling, Maximum Likelihood and minimum divergence estimators

Abstract

This paper explores Maximum Likelihood in parametric models in the context of Sanov type Large Deviation Probabilities. MLE in parametric models under weighted sampling is shown to be associated with the minimization of a specific divergence criterion defined with respect to the distribution of the weights. Some properties of the resulting inferential procedure are presented; Bahadur efficiency of tests are also considered in this context.