A Wald-type test statistic based on robust modified median estimator in logistic regression models

ABSTRACT

In this paper a new robust estimator, modified median estimator, is introduced and studied for the logistic regression model. This estimator is based on the median estimator considered in Hobza et al. [Robust median estimator in logistic regression. J Stat Plan Inference. 2008;138:3822–3840]. Its asymptotic distribution is obtained. Using the modified median estimator, we also consider a Wald-type test statistic for testing linear hypotheses in the logistic regression model and we obtain its asymptotic distribution under the assumption of random regressors. An extensive simulation study is presented in order to analyse the efficiency as well as the robustness of the modified median estimator and Wald-type test based on it.

KEYWORDS:

• Logistic regression
• modified median estimator
• random regressors
• Wald-type test statistic

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F35
• 62F05

Acknowledgements

We would like to thank the referees for their helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was partially supported by the Spanish grant MTM2015-67057-P provided by Ministerio de Economía y Competittividad and the Czech grants 15-15049S provided by Grantová agentura České republiky and SGS15/214/OHK4/3T/14 provided by Ministerstvo Školství, Mládeže a Tělovýchovy.