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Testing Distributional Inequalities and Asymptotic Bias

  • Kyungchul Song

    ()

    (Department of Economics, University of Pennsylvania)

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    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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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/08-005.pdf
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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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    Length: 28 pages
    Date of creation: 19 Feb 2008
    Date of revision:
    Handle: RePEc:pen:papers:08-005
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    1. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
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