Weighted sampling, Maximum Likelihood and minimum divergence estimators

2012/07/27 by Michel Broniatowski, Broniatowski, Michel, Zhansheng Cao +1
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1207.6606

openalex publication_date 2012/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Minimum divergence estimators, maximum likelihood and exponential families
• Divergence and Model Adequacy, A Semiparametric Case Study
• Parametric estimation and tests through divergences and duality technique
• Statistical Inference based on Bridge Divergences
• Statistical Inference Based on a New Weighted Likelihood Approach