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2017 A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator
Ayanendranath Basu, Abhik Ghosh, Abhijit Mandal, Nirian Martín, Leandro Pardo
Electron. J. Statist. 11(2): 2741-2772 (2017). DOI: 10.1214/17-EJS1295

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. A family of robust Wald type tests are considered here, where the minimum density power divergence estimator is used instead of the maximum likelihood estimator. We obtain the asymptotic distribution and also study the robustness properties of these Wald type test statistics. 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.

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Ayanendranath Basu. Abhik Ghosh. Abhijit Mandal. Nirian Martín. Leandro Pardo. "A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator." Electron. J. Statist. 11 (2) 2741 - 2772, 2017. https://doi.org/10.1214/17-EJS1295

Information

Received: 1 July 2016; Published: 2017
First available in Project Euclid: 4 July 2017

zbMATH: 1366.62052
MathSciNet: MR3679908
Digital Object Identifier: 10.1214/17-EJS1295

Subjects:
Primary: 62F35, 662F05

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Vol.11 • No. 2 • 2017
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