Several Applications of Divergence Criteria in Continuous Families

Michel Broniatowski; Igor Vajda

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arXiv · 0911.0937

Several Applications of Divergence Criteria in Continuous Families

Michel Broniatowski·Igor Vajda

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Abstract

This paper deals with four types of point estimators based on minimization of information-theoretic divergences between hypothetical and empirical distributions. These were introduced (i) by Liese & Vajda (2006) and independently Broniatowski & Keziou (2006), called here power superdivergence estimators, (ii) by Broniatowski & Keziou (2009), called here power subdivergence estimators, (iii) by Basu et al. (1998), called here power pseudodistance estimators, and (iv) by Vajda (2008) called here Renyi pseudodistance estimators. The paper studies and compares general properties of these estimators such as consistency and influence curves, and illustrates these properties by detailed analysis of the applications to the estimation of normal location and scale.

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Michel Broniatowski, Igor Vajda. 2009-11-04. Several Applications of Divergence Criteria in Continuous Families. https://arxiv.org/abs/0911.0937

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