An improved bootstrap test of stochastic dominance

• Published in: Econometrics 2010-02, Vol.154 (2), p.186-202
• Main Authors: Linton, Oliver, Song, Kyungchul, Whang, Yoon-Jae
• Format: Article
• Language: English
• Subjects: Applications; Bootstrap; Bootstrap mechanism; Bootstrap method; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Economic models; Estimation; Exact sciences and technology; Experimental design; Inequality; Inequality restrictions; Insurance, economics, finance; Mathematics; Parametric inference; Probability; Probability and statistics; Sciences and techniques of general use; Set estimation; Simulation; Statistics; Stochastic dominance; Stochastic dominance Inequality restrictions Bootstrap Set estimation; Stochastic models; Stochastic processes; Studies
• ISSN: 0304-4076; 2225-1146; 1872-6895; 2225-1146
• DOI: 10.1016/j.jeconom.2009.08.002

We propose a new method of testing stochastic dominance that improves on existing tests based on the standard bootstrap or subsampling. The method admits prospects involving infinite as well as finite dimensional unknown parameters, so that the variables are allowed to be residuals from nonparametric and semiparametric models. The proposed bootstrap tests have asymptotic sizes that are less than or equal to the nominal level uniformly over probabilities in the null hypothesis under regularity conditions. This paper also characterizes the set of probabilities so that the asymptotic size is exactly equal to the nominal level uniformly. As our simulation results show, these characteristics of our tests lead to an improved power property in general. The improvement stems from the design of the bootstrap test whose limiting behavior mimics the discontinuity of the original test’s limiting distribution.