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Phi-divergence statistics for the likelihood ratio order: An approach based on log-linear models

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Martín Apaolaza, Níriam and Mata, Raquel and Pardo Llorente, Leandro (2014) Phi-divergence statistics for the likelihood ratio order: An approach based on log-linear models. Journal of multivariate analysis, 130 . pp. 387-408. ISSN 0047-259X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0047259X14001341


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Abstract

When some treatments are ordered according to the categories of an ordinal categorical variable (e.g., extent of side effects) in a monotone order, one might be interested in knowing whether the treatments are equally effective or not. One way to do that is to test if the likelihood ratio order is strictly verified. A method based on log-linear models is derived to make statistical inference and phi-divergence test-statistics are proposed for the test of interest. Focused on log-linear modeling, the theory associated with the asymptotic distribution of the phi-divergence test-statistics is developed. An illustrative example motivates the procedure and a simulation study for small and moderate sample sizes shows that it is possible to find phi-divergence test-statistic with an exact size closer to nominal size and higher power in comparison with the classical likelihood ratio.


Item Type:Article
Uncontrolled Keywords:Phi-divergence test statistics; Inequality constrains; Likelihood ratio ordering; Log-linear modeling
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:26687
Deposited On:11 Sep 2014 09:25
Last Modified:11 Sep 2014 09:25

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