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On the robustness of a divergence based test of simple statistical hypotheses

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Ghosh, A. and Basu, A. and Pardo Llorente, Leandro (2015) On the robustness of a divergence based test of simple statistical hypotheses. Journal of Statistical Planning and Inference, 161 . pp. 91-108. ISSN 0378-3758

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Official URL: http://www.sciencedirect.com/science/article/pii/S0378375815000051




Abstract

The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density power divergence; however, although the robustness properties of the latter test were intuitively argued for by the authors together with extensive empirical substantiation of the same, no theoretical robustness properties were presented in this work. In the present paper we will consider a more general class of tests which form a superfamily of the procedures described by Basu et al. (2013a). This superfamily derives from the class of S-divergences recently proposed by Basu et al. (2013a). In this context we theoretically prove several robustness results of the new class of tests and illustrate them in the normal model. All the theoretical robustness properties of the Basu et al. (2013a) proposal follows as special cases of our results.


Item Type:Article
Uncontrolled Keywords:Hypothesis testing; Robustness; S-divergence
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:30290
Deposited On:22 May 2015 08:17
Last Modified:22 May 2015 12:05

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