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Empirical phi-divergence test statistics for testing simple and composite null hypotheses

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Balakrishnan, Narayanaswamy and Martin, Nirian and Pardo Llorente, Leandro (2015) Empirical phi-divergence test statistics for testing simple and composite null hypotheses. Statistics: A Journal of Theoretical and Applied Statistics, 49 (5). pp. 951-977. ISSN 0233-1888

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/02331888.2014.957702


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Abstract

The main purpose of this paper is to introduce first a new family of empirical test statistics for testing a simple null hypothesis when the vector of parameters of interest is defined through a specific set of unbiased estimating functions. This family of test statistics is based on a distance between two probability vectors, with the first probability vector obtained by maximizing the empirical likelihood (EL) on the vector of parameters, and the second vector defined from the fixed vector of parameters under the simple null hypothesis. The distance considered for this purpose is the phi-divergence measure. The asymptotic distribution is then derived for this family of test statistics. The proposed methodology is illustrated through the well-known data of Newcomb's measurements on the passage time for light. A simulation study is carried out to compare its performance with that of the EL ratio test when confidence intervals are constructed based on the respective statistics for small sample sizes. The results suggest that the empirical modified likelihood ratio test statistic' provides a competitive alternative to the EL ratio test statistic, and is also more robust than the EL ratio test statistic in the presence of contamination in the data. Finally, we propose empirical phi-divergence test statistics for testing a composite null hypothesis and present some asymptotic as well as simulation results for evaluating the performance of these test procedures.


Item Type:Article
Uncontrolled Keywords:Empirical likelihood, Empirical phi-divergence test statistics, Influence function, Phi-divergence measures, Power function, Empirical likelihood ratio, Empirical modified likelihood ratio.
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:33258
Deposited On:24 Sep 2015 06:49
Last Modified:24 Sep 2015 06:49

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