Restricted distance-type Gaussian estimators based on density power divergence and their applications in hypothesis testing

TL;DR

This paper introduces a restricted minimum density power divergence Gaussian estimator (MDPDGE) that enhances robustness and applicability in hypothesis testing for models with unknown likelihoods, supported by theoretical and empirical analysis.

Contribution

It develops the MDPDGE with asymptotic properties, robustness analysis, and robust Rao-type tests, extending existing methods to constrained estimation scenarios.

Findings

The MDPDGE is robust against data contamination.

The proposed tests perform well in simulations.

Explicit distribution expressions are derived for practical use.

Abstract

Zhang (2019) presented a general estimation approach based on the Gaussian distribution for general parametric models where the likelihood of the data is difficult to obtain or unknown, but the mean and variance-covariance matrix are known. Castilla and Zografos (2021) extended the method to density power divergence-based estimators, which are more robust than the likelihood-based Gaussian estimator against data contamination. In this paper we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. Also, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, in special in testing composite null hypothesis, and provide here constrained estimators to inherent restrictions of the underlying distribution. Further, we derive robust Rao-type test statistics based on the MDPDGE for testing simple null hypothesis and we deduce explicit expressions for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the method through a simulation study.