Alternative forms and properties of the score test

Abstract
TWO different issues relating to the score (S) test are investigated. Firstly, we study the finite sample properties of a number of asymptotically equivalent forms of the S test. From our simulation results we observe that these forms can behave very differently in finite samples. Secondly, we investigate the power properties of the S test and find that it compares favorably to those of the likelihood ratio (LR) test although the former does not use information about the precise forms of the alternatives.