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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| Veröffentlicht in: | Journal of statistical planning and inference Jg. 161; S. 91 - 108 |
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01.06.2015
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| 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 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. |
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| AbstractList | 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. |
| Author | Basu, Ayanendranath Ghosh, Abhik Pardo, Leandro |
| Author_xml | – sequence: 1 givenname: Abhik surname: Ghosh fullname: Ghosh, Abhik email: abhianik@gmail.com organization: Indian Statistical Institute, Kolkata, India – sequence: 2 givenname: Ayanendranath surname: Basu fullname: Basu, Ayanendranath email: ayanbasu@isical.ac.in organization: Indian Statistical Institute, Kolkata, India – sequence: 3 givenname: Leandro surname: Pardo fullname: Pardo, Leandro email: lpardo@mat.ucm.es organization: Complutense University, Madrid, Spain |
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| Cites_doi | 10.1111/j.2517-6161.1984.tb01318.x 10.1007/s10463-012-0372-y 10.1098/rsta.1933.0009 10.1016/j.csda.2008.11.025 10.1017/S030500410001152X 10.1016/j.jmva.2010.07.010 10.1214/aoms/1177732360 10.1214/aoms/1177699531 10.1080/01621459.1994.10476822 10.1214/aoms/1177693437 10.1214/aos/1176325512 10.1214/15-EJS1025 10.1016/0771-050X(81)90013-9 10.1093/biomet/85.3.549 10.2307/2342435 10.1214/aoms/1177698877 10.1214/aoms/1177698878 |
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