The Logarithmic Super Divergence and Statistical Inference : Asymptotic Properties

TL;DR

This paper explores the asymptotic properties of inference methods based on the recently introduced logarithmic super divergence family, which generalizes several existing divergence measures, with validation through real data examples.

Contribution

It characterizes the asymptotic behavior of inference procedures derived from the LSD family in discrete models, expanding understanding of its theoretical properties.

Findings

Asymptotic properties are established for LSD-based inference.

Real data examples support the theoretical results.

LSD acts as a superfamily encompassing LPD and LDPD divergences.

Abstract

Statistical inference based on divergence measures have a long history. Recently, Maji, Ghosh and Basu (2014) have introduced a general family of divergences called the logarithmic super divergence (LSD) family. This family acts as a superfamily for both of the logarithmic power divergence (LPD) family (eg. Renyi, 1961) and the logarithmic density power divergence (LDPD)family introduced by Jones et al. (2001). In this paper we describe the asymptotic properties of the inference procedures resulting from this divergence in discrete models. The properties are well supported by real data examples.