Testing Distributional Inequalities and Asymptotic Bias

When Barret and Donald (2003) in Econometrica proposed a consistent test of stochastic dominance, they were silent about the asymptotic unbiasedness of their tests against √n-converging Pitman local alternatives. This paper shows that when we focus on first-order stochastic dominance, there exists a wide class of√n-converging Pitman local alternatives against which their test is asymptotically biased, i.e., having the local asymptotic power strictly below the asymptotic size. This phenomenon more generally applies to one-sided nonparametric tests which have a sup norm of a shifted standard Brownian bridge as their limit under√n-converging Pitman local alternatives. Among other examples are tests of independence or conditional independence. We provide an intuitive explanation behind this phenomenon, and illustrate the implications using the simulation studies.

Download Paper

Paper Number
08-005
Year
2008
Authored by