A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator

TL;DR

This paper introduces a robust Wald-type test for linear hypotheses in logistic regression using the minimum density power divergence estimator, demonstrating improved stability against data contamination.

Contribution

It develops a new robust Wald-type test based on the minimum density power divergence estimator for logistic regression, with theoretical and empirical validation.

Findings

The proposed test maintains stability under data contamination.

The classical Wald test is less robust and breaks down with contamination.

Simulation results confirm the theoretical robustness and effectiveness.

Abstract

In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates although some ideas with non random covariates are also considered. The family of tests considered is based on the minimum density power divergence estimator instead of the maximum likelihood estimator and it is referred to as the Wald-type test statistic in the paper. We obtain the asymptotic distribution and also study the robustness properties of the Wald type test statistic. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.