Weighted sampling, Maximum Likelihood and minimum divergence estimators
Michel Broniatowski, Zhansheng Cao
TL;DR
This paper investigates the properties of Maximum Likelihood Estimation under weighted sampling, linking it to divergence minimization and analyzing its efficiency in the context of large deviations.
Contribution
It introduces a divergence-based interpretation of weighted MLE and examines its statistical properties and efficiency, extending classical MLE theory to weighted sampling scenarios.
Findings
Weighted MLE corresponds to divergence minimization.
Properties of weighted MLE are characterized.
Bahadur efficiency of tests under weighted sampling is analyzed.
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.
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Taxonomy
TopicsAdvanced Statistical Methods and Models · Statistical Methods and Inference · Bayesian Methods and Mixture Models