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An adaptive test of stochastic monotonicity

Authors: Denis Chetverikov , Daniel Wilhelm and Dongwoo Kim
Date: 03 April 2018
Type: cemmap Working Paper, CWP24/18
DOI: 10.1920/wp.cem.2018.2418

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 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 fi nite samples. In particular, the simulations show that the test controls size and may be signi ficantly more powerful than existing alternative procedures.

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