  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 are 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 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 empirical likelihood
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 empirical likelihood ratio test statistic, and is also more robust than the
empirical likelihood 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.
