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

TL;DR

This paper develops the asymptotic properties of minimum S-Divergence estimators for continuous models using the Basu-Lindsay smoothing approach, demonstrating their efficiency and robustness through simulations and real data examples.

Contribution

It introduces the asymptotic analysis of minimum S-Divergence estimators under continuous models using a novel smoothing approach that simplifies kernel bandwidth selection.

Findings

Estimators show strong robustness against model deviations.

Simulation studies confirm high efficiency of the estimators.

Real data examples demonstrate practical applicability.

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.