Testing Distributional Inequalities and Asymptotic Bias
AbstractWhen 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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Bibliographic InfoPaper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 08-005.
Length: 28 pages
Date of creation: 19 Feb 2008
Date of revision:
Asymptotic Bias; One-sided Tests; Stochastic Dominance; Conditional Independence; Pitman Local Alternatives; Brownian Bridge Processes;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
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- Oliver Linton1 & Kyungchul Song & Yoon-Jae Whang, 2008.
"Bootstrap Tests of Stochastic Dominance with Asymptotic Similarity on the Boundary,"
PIER Working Paper Archive
08-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Oliver Linton & Kyungchul Song & Yoon-Jae Whang, 2008. "Bootstrap tests of stochastic dominance with asymptotic similarity on the boundary," CeMMAP working papers CWP08/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Oliver Linton & Kyungchul Song & Yoon-Jae Whang, 2008. "Bootstrap Tests of Stochastic Dominance with AsymptoticSimilarity on the Boundary," STICERD - Econometrics Paper Series /2008/527, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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