Generalized score tests for composite hypotheses

Abstract Three large sample tests, namely, Rao’s likelihood score test, Neyman’s C(α) test and a generalized score test are reviewed in a unified general setting involving possibly dependent, and not necessarily identically distributed observations. An application to a first-order autoregressive-moving average model is discussed. The test statistics considered in this paper are based on certain estimating functions. The Rao statistic is based on the likelihood estimating function and the Neyman statistic requires partly a general score function and partly the likelihood estimating function. The general score test is based on an arbitrary estimating function. It is shown in the application that the choice of an optimal estimating function according to the Godambe criterion also leads to asymptotical optimal tests for composite hypotheses.