Testing for Stochastic Monotonicity
提出一种检验随机单调性的方法，基于U统计量的上确界，其渐近分布为Gumbel分布，并改进了有限样本近似。该方法可用于研究代际收入流动性等经济问题。
We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications in economics. 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. We also propose a refinement to the asymptotic approximation that we show works much better in finite samples. We apply our test to the study of intergenerational income mobility. Copyright 2009 The Econometric Society.