Testing Distributional Inequalities and Asymptotic Bias

Kyungchul Song ()
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Kyungchul Song: Department of Economics, University of Pennsylvania

PIER Working Paper Archive from Penn Institute for Economic Research, 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.

Keywords: Asymptotic Bias; One-sided Tests; Stochastic Dominance; Conditional Independence; Pitman Local Alternatives; Brownian Bridge Processes (search for similar items in EconPapers)
JEL-codes: C12 C14 C52 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2008-02-19
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (4)

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