This paper studies the Hodges and Lehmann (1956) optimality of tests in a general setup. The tests are compared by the exponential rates of growth to one of the power functions evaluated at a fixed alternative while keeping the asymptotic sizes bounded by some constant. We present two sets of...

In this paper we make two contributions. First, we show by example that empirical likelihood and other commonly used tests for parametric moment restrictions, including the GMM-based J-test of Hansen (1982), are unable to control the rate at which the probability of a Type I error tends to zero....