Several Applications of Divergence Criteria in Continuous Families

TL;DR

This paper compares four types of divergence-based point estimators in continuous families, analyzing their properties like consistency and influence, with detailed applications to normal distribution parameters.

Contribution

It provides a comparative study of four divergence-based estimators, highlighting their theoretical properties and practical applications in estimating normal distribution parameters.

Findings

All estimators exhibit consistency under certain conditions.

Influence functions vary among estimators, affecting robustness.

Applications to normal distributions demonstrate differences in efficiency.

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.