A Comparison of Likelihood Ratio, Wald, and Rao Tests

Abstract

Three commonly considered methods for forming approximate (large-sample) tests of a simple null hypothesis are: (a) the likelihood ratio test, (b) the Wald “linearization” test, and (c) a quadratic scores test due to Rao. In the context of testing that the variance of a normal distribution is equal to one, it is possible to make detailed finite-sample power comparisons, both “local” and “nonlocal,” of these tests. In contrast to at least one assertion made in the literature (Chandra and Joshi, 1983), none of the three tests dominates another, even locally.