The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach

Abstract

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures for robust statistical inference, named the S-Divergence Family. Ghosh (2014) discussed its asymptotic properties for the discrete model of densities. In the present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under continuous models. Here we use the Basu-Lindsay approach (1994) of smoothing the model densities that, unlike previous approaches, avoids much of the complications of the kernel bandwidth selection. Illustrations are presented to support the performance of the resulting estimators both in terms of efficiency and robustness through extensive simulation studies and real data examples.

Pre-Print, 34 pages

References in corpus (4)

• Robust Estimation in Generalised Linear Models : The Density Power Divergence Approach
• On the Robustness of a Divergence based Test of Simple Statistical Hypotheses
• Testing Composite Hypothesis based on the Density Power Divergence
• Asymptotic Properties of Minimum S-Divergence Estimator for Discrete Models

Cited by in corpus (4)

• Influence Function Analysis of the Restricted Minimum Divergence Estimators : A General Form
• A New Family of Divergences Originating from Model Adequacy Tests and Application to Robust Statistical Inference
• Testing Composite Null Hypothesis Based on $S$-Divergences
• Improvements in the Small Sample Efficiency of the Minimum $S$-Divergence Estimators under Discrete Models