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The main purpose of this paper is to introduce first a new family ofempirical test statistics for testing a simple null hypothesis when the vectorof parameters of interest are defined through a specific set of unbiasedestimating functions. This family of test statistics is based on a distancebetween two probability vectors, with the first probability vector obtained bymaximizing the empirical likelihood on the vector of parameters, and the secondvector defined from the fixed vector of parameters under the simple nullhypothesis. The distance considered for this purpose is the phi-divergencemeasure. The asymptotic distribution is then derived for this family of teststatistics. The proposed methodology is illustrated through the well-known dataof Newcomb's measurements on the passage time for light. A simulation study iscarried out to compare its performance with that of the empirical likelihoodratio test when confidence intervals are constructed based on the respectivestatistics for small sample sizes. The results suggest that the "empiricalmodified likelihood ratio test statistic" provides a competitive alternative tothe empirical likelihood ratio test statistic, and is also more robust than theempirical likelihood ratio test statistic in the presence of contamination inthe data. Finally, we propose empirical phi-divergence test statistics fortesting a composite null hypothesis and present some asymptotic as well assimulation results for evaluating the performance of these test procedures.

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