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An Adaptive Test Of Stochastic Monotonicity

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  • Chetverikov, Denis
  • Wilhelm, Daniel
  • Kim, Dongwoo

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.

Suggested Citation

  • Chetverikov, Denis & Wilhelm, Daniel & Kim, Dongwoo, 2021. "An Adaptive Test Of Stochastic Monotonicity," Econometric Theory, Cambridge University Press, vol. 37(3), pages 495-536, June.
    • Handle: RePEc:cup:etheor:v:37:y:2021:i:3:p:495-536_3
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    Cited by:

    1. Denis Chetverikov & Dongwoo Kim & Daniel Wilhelm, 2018. "Nonparametric instrumental-variable estimation," Stata Journal, StataCorp LLC, vol. 18(4), pages 937-950, December.
    2. Daniel Wilhelm, 2018. "Testing for the presence of measurement error," CeMMAP working papers CWP45/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Henry, Marc & Méango, Romuald & Mourifié, Ismaël, 2024. "Role models and revealed gender-specific costs of STEM in an extended Roy model of major choice," Journal of Econometrics, Elsevier, vol. 238(2).
    4. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2019. "Improved Central Limit Theorem and bootstrap approximations in high dimensions," Papers 1912.10529, arXiv.org, revised May 2022.

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