TESTING HYPOTHESES WITH ESTIMATED SCORES

A method is proposed for testing hypotheses that is very much in the spirit of expected maximum log likelihood estimation and bears much the same relation to it as the likelihood ratio test methodology does to maximum likelihood estimation. For a single test parameter, the method amounts to basing critical regions on the difference between the estimated score and its expectation. In some cases where a sufficient statistic, independent of the test parameter, exists for the nuisance parameter, the test coincides with that based on the conditional distribution. An approximate approach is described for complicated situations, with algebraic examination of the scalar test and nuisance parameter case and examples of the vector parameter case.