Influence Analysis of Robust Wald-type Tests

TL;DR

This paper introduces a robust Wald-type test using minimum density power divergence estimators, demonstrating improved stability against outliers compared to classical Wald tests through theoretical analysis and numerical examples.

Contribution

It develops a new robust Wald test framework based on density power divergence estimators, enhancing robustness in hypothesis testing.

Findings

Robust Wald tests are stable against outliers.

Classical Wald tests break down with outliers.

Numerical examples confirm theoretical robustness.

Abstract

We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of the maximum likelihood estimators. An extensive study of their robustness properties is given though the influence functions as well as the chi-square inflation factors. It is theoretically established that the level and power of these robust tests are stable against outliers, whereas the classical Wald test breaks down. Some numerical examples confirm the validity of the theoretical results.