On Generalized Score Tests

Abstract Generalizations of Rao's score test are receiving increased attention, especially in the econometrics and biostatistics literature. These generalizations are able to account for certain model inadequacies or lack of knowledge by use of empirical variance estimates. This article shows how the various forms of the generalized test statistic arise from Taylor expansion of the estimating equations. The general estimating equations structure unifies a variety of applications and helps suggest new areas of application.