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Comparing two treatments in terms of the likelihood ratio order

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Martín, Nazario and Mata Crespo, Raquel and Pardo Llorente, Leandro (2015) Comparing two treatments in terms of the likelihood ratio order. Journal of Statistical Computation and Simulation, 85 (17). pp. 3512-3534. ISSN 0094-9655

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/00949655.2014.984187#.VPghZfmG-Ck




Abstract

In this paper new families of test statistics are introduced and studied for the problem of comparing two treatments in terms of the likelihood ratio order. The considered families are based on phi-divergence measures and arise as natural extensions of the classical likelihood ratio test and Pearson test statistics. It is proven that their asymptotic distribution is a common chi-bar random variable. An illustrative example is presented and the performance of these statistics is analysed through a simulation study. Through a simulation study it is shown that, for most of the proposed scenarios adjusted to be small or moderate, some members of this new family of test-statistic display clearly better performance with respect to the power in comparison to the classical likelihood ratio and the Pearson's chi-square test while the exact size remains closed to the nominal size. In view of the exact powers and significance levels, the study also shows that the Wilcoxon test-statistic is not as good as the two classical test-statistics.


Item Type:Article
Uncontrolled Keywords:divergence measure, Kullback divergence measure, inequality constrains, likelihood ratioorder, loglinear models, 62H17
Subjects:Sciences > Mathematics
ID Code:29045
Deposited On:05 Mar 2015 09:31
Last Modified:07 Mar 2017 12:33

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