An Adaptive Test of Stochastic Monotonicity

Denis Chetverikov (), Daniel Wilhelm and Dongwoo Kim
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Denis Chetverikov: Institute for Fiscal Studies and UCLA

No CWP17/20, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: We propose a new nonparametric test of stochastic monotonicity which adapts to the unknown smoothness of the conditional distribution of interest, possesses desirable asymptotic properties, is conceptually easy to implement, and computationally attractive. In particular, we show that the test asymptotically controls size at a polynomial rate, is non-conservative, and detects certain smooth local alternatives that converge to the null with the fastest possible rate. Our test is based on a data-driven bandwidth value and the critical value for the test takes this randomness into account. Monte Carlo simulations indicate that the test performs well in ?nite samples. In particular, the simulations show that the test controls size and, under some alternatives, is signi?cantly more powerful than existing procedures.

Date: 2020-05-04
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Related works:
Journal Article: AN ADAPTIVE TEST OF STOCHASTIC MONOTONICITY (2021)
Working Paper: An adaptive test of stochastic monotonicity (2019)
Working Paper: An adaptive test of stochastic monotonicity (2018)
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