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Tests of stochastic monotonicity with improved power

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  • Seo, Juwon

Abstract

We develop improved statistical procedures for testing stochastic monotonicity. While existing tests use a fixed critical value to set the limiting rejection rate equal to nominal size at the least favorable case, we use a bootstrap procedure to raise the limiting rejection rate to nominal size over much of the null. This improves power against relevant local alternatives. To show the validity of our approach we draw on recent results on the directional differentiability of the least concave majorant operator, and on bootstrap inference when smoothness conditions sufficient to apply the functional delta method for the bootstrap are not satisfied.

Suggested Citation

  • Seo, Juwon, 2018. "Tests of stochastic monotonicity with improved power," Journal of Econometrics, Elsevier, vol. 207(1), pages 53-70.
    • Handle: RePEc:eee:econom:v:207:y:2018:i:1:p:53-70
    DOI: 10.1016/j.jeconom.2018.04.004
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    Cited by:

    1. Hongyi Jiang & Zhenting Sun & Shiyun Hu, 2023. "A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance," Papers 2306.12271, arXiv.org, revised Jul 2023.
    2. 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.
    3. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    4. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.
    5. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    6. Sungwon Lee, 2021. "Partial Identification and Inference for Conditional Distributions of Treatment Effects," Papers 2108.00723, arXiv.org, revised Nov 2023.
    7. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.
    8. Sungwon Lee, 2024. "Partial identification and inference for conditional distributions of treatment effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 107-127, January.

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    More about this item

    Keywords

    Stochastic monotonicity; Copula; Least concave majorant; Hadamard differentiability; Hadamard directional differentiability;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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