Asymptotic breakdown point analysis of the minimum density power divergence estimator under independent non-homogeneous setups

TL;DR

This paper extends the analysis of the robustness of the minimum density power divergence estimator (MDPDE) to independent non-homogeneous data, providing theoretical bounds and empirical validation for its global reliability.

Contribution

It introduces the asymptotic breakdown point analysis of MDPDE under INH setups, a novel theoretical contribution in robust statistics.

Findings

Derived a lower bound for the asymptotic breakdown point of MDPDE

Validated theoretical results with simulation studies

Applied findings to fixed design regression models

Abstract

The minimum density power divergence estimator (MDPDE) has gained significant attention in the literature of robust inference due to its strong robustness properties and high asymptotic efficiency; it is relatively easy to compute and can be interpreted as a generalization of the classical maximum likelihood estimator. It has been successfully applied in various setups, including the case of independent and non-homogeneous (INH) observations that cover both classification and regression-type problems with a fixed design. While the local robustness of this estimator has been theoretically validated through the bounded influence function, no general result is known about the global reliability or the breakdown behavior of this estimator under the INH setup, except for the specific case of location-type models. In this paper, we extend the notion of asymptotic breakdown point from the case of independent and identically distributed data to the INH setup and derive a theoretical lower bound for the asymptotic breakdown point of the MDPDE, under some easily verifiable assumptions. These results are further illustrated with applications to some fixed design regression models and corroborated through extensive simulation studies.