Wald type and Phi-divergence based test-statistics for isotonic binomial   proportions
  In this paper new test statistics are introduced and studied for the important problem of testing hypothesis that involves inequality constraint on proportions when the sample comes from independent binomial random variables: Wald type and phi-divergence based test-statistics. As a particular case of phi-divergence based test-statistics, the classical likelihood ratio test is considered. An illustrative example is given and the performance of all of them for small and moderate sample sizes is analyzed in an extensive simulation study. 
Nirian Mart\'in, Raquel Mata, Leando Pardo
stat.ME