Kyungchul Song () (Department of Economics, University of Pennsylvania)
Abstract
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.
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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number
08-005.
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