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An adaptive test of stochastic monotonicity

Authors: Denis Chetverikov , Daniel Wilhelm and Dongwoo Kim
Date: 15 October 2019
Type: cemmap Working Paper, CWP49/19
DOI: 10.1920/wp.cem.2019.4919

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 finite samples. In particular, the simulations show that the test controls size and, under some alternatives, is significantly more powerful than existing procedures.

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Previous version:
Denis Chetverikov, Daniel Wilhelm and Dongwoo Kim April 2018, An adaptive test of stochastic monotonicity, cemmap Working Paper, The IFS

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