A New Class of Robust Two-Sample Wald-Type Tests

Ghosh Abhik, Martin Nirian, Basu Ayanendranath () and Pardo Leandro
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Ghosh Abhik: Kolkata Interdisciplinary Statistical Research Unit 203, Indian Statistical Institute, B. T. Road, Kolkata- 700108, India
Martin Nirian: Departamento de Estadistica e I.O., Complutense University of Madrid, II Avenida de Islas Filipinas 3, Madrid28003, Spain
Basu Ayanendranath: Kolkata Interdisciplinary Statistical Research Unit 203, Indian Statistical Institute, B. T. Road, Kolkata- 700108, India
Pardo Leandro: Departamento de Estadistica e I.O., Complutense University of Madrid, Plaza de Ciencias 3, Madrid28040, Spain

The International Journal of Biostatistics, 2018, vol. 14, issue 2, 29

Abstract: Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for testing such two sample problems using the minimum density power divergence estimators of the underlying parameters. In particular, we consider the simple two-sample hypothesis concerning the full parametric homogeneity as well as the general two-sample (composite) hypotheses involving some nuisance parameters. The asymptotic and theoretical robustness properties of the proposed Wald-type tests have been developed for both the simple and general composite hypotheses. Some particular cases of testing against one-sided alternatives are discussed with specific attention to testing the effectiveness of a treatment in clinical trials. Performances of the proposed tests have also been illustrated numerically through appropriate real data examples.

Keywords: robust hypothesis testing; two-sample problems; minimum density power divergence estimator; influence function; clinical trial (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1515/ijb-2017-0023

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