Power and Level Robustness of A Composite Hypothesis Testing under Independent Non-Homogeneous Data

TL;DR

This paper evaluates the robustness of a new class of composite hypothesis tests based on density power divergence under independent non-homogeneous data, providing theoretical influence function analysis and empirical validation.

Contribution

It offers a rigorous derivation of power and level influence functions for these tests, establishing their robustness properties and applying them to linear regression models.

Findings

The tests exhibit bounded influence functions indicating robustness.

Theoretical analysis confirms stability of size and power under data contamination.

Empirical results support the robustness and applicability of the proposed tests.

Abstract

Robust tests of general composite hypothesis under non-identically distributed observations is always a challenge. Ghosh and Basu (2018, Statistica Sinica, 28, 1133--1155) have proposed a new class of test statistics for such problems based on the density power divergence, but their robustness with respect to the size and power are not studied in detail. This note fills this gap by providing a rigorous derivation of power and level influence functions of these tests to theoretically justify their robustness. Applications to the fixed-carrier linear regression model are also provided with empirical illustrations.