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AN ADAPTIVE TEST OF STOCHASTIC MONOTONICITY

Published online by Cambridge University Press:  16 June 2020

Denis Chetverikov ,
Daniel Wilhelm  and
Dongwoo Kim
Denis Chetverikov
Affiliation:
University of California at Los Angeles
Daniel Wilhelm*
Affiliation:
University College London
Dongwoo Kim
Affiliation:
Simon Fraser University
*
Address correspondence to Daniel Wilhelm, Department of Economics, University College London, Gower Street, LondonWC1E 6BT, United Kingdom; e-mail: d.wilhelm@ucl.ac.uk.
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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 nonconservative, 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.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 3 , June 2021 , pp. 495 - 536
Copyright
© Cambridge University Press 2020

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Footnotes

*

We thank Ivan Canay and Whitney Newey for useful comments. Daniel Wilhelm gratefully acknowledges financial support from the ESRC Centre for Microdata Methods and Practice at IFS (RES-589-28-0001) and the European Research Council (ERC-2014-CoG-646917-ROMIA).

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