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Testing for stochastic monotonicity

Authors: Sokbae (Simon) Lee , Oliver Linton and Yoon-Jae Whang
Date: 09 August 2006
Type: External publication,


We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part and so we have to extend existing results that only apply to either one or the other case.

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