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

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...

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Bibliographic Details
Published in:Journal of statistical planning and inference Vol. 161; pp. 91 - 108
Main Authors: Ghosh, Abhik, Basu, Ayanendranath, Pardo, Leandro
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2015
Subjects:
[formula omitted]-divergence
Hypothesis testing
Robustness
Hypothesis testing
Robustness
S-divergence
ISSN:0378-3758, 1873-1171
Online Access:Get full text
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Summary: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 that work. In the present paper we will consider a more general class of tests which forms a superfamily of the procedures described by Basu et al. (2013a). This superfamily derives from the class of S-divergences recently proposed by Ghosh et al. (2013). 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. •Generalizes DPD based tests to the case of the S-divergence.•Presents theoretical robustness results for S-divergence based tests.•Derives the power and level influence functions of the tests.•Introduces the chi-square inflation factor in connection with the S-divergence tests.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2015.01.003