## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 11, Number 2 (2017), 2741-2772.

### 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, and Leandro Pardo

#### 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.

#### Article information

**Source**

Electron. J. Statist., Volume 11, Number 2 (2017), 2741-2772.

**Dates**

Received: July 2016

First available in Project Euclid: 4 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1499133753

**Digital Object Identifier**

doi:10.1214/17-EJS1295

**Mathematical Reviews number (MathSciNet)**

MR3679908

**Zentralblatt MATH identifier**

1366.62052

**Subjects**

Primary: 62F35: Robustness and adaptive procedures 662F05

**Keywords**

Influence function logistic regression minimum density power divergence estimators random explanatory variables robustness Wald-type test statistics

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Basu, Ayanendranath; Ghosh, Abhik; Mandal, Abhijit; Martín, Nirian; Pardo, Leandro. A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator. Electron. J. Statist. 11 (2017), no. 2, 2741--2772. doi:10.1214/17-EJS1295. https://projecteuclid.org/euclid.ejs/1499133753