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An improved bootstrap test of density ratio ordering

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  • Beare, Brendan K.
  • Shi, Xiaoxia

Abstract

Two probability distributions with common support are said to exhibit density ratio ordering when they admit a nonincreasing density ratio. Existing statistical tests of the null hypothesis of density ratio ordering are known to be conservative, with null limiting rejection rates below the nominal significance level whenever the two distributions are unequal. It is shown that a bootstrap procedure can be used to raise the pointwise limiting rejection rate to the nominal significance level on the boundary of the null. This improves power against nearby alternatives. The proposed procedure is based on preliminary estimation of a contact set, the form of which is obtained from a novel representation of the Hadamard directional derivative of the least concave majorant operator. Numerical simulations indicate that improvements to power can be very large in moderately sized samples.

Suggested Citation

  • Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    • Handle: RePEc:eee:ecosta:v:10:y:2019:i:c:p:9-26
    DOI: 10.1016/j.ecosta.2018.08.002
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    Cited by:

    1. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    2. 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.
    3. Xavier D'Haultfoeuille & Christophe Gaillac & Arnaud Maurel, 2021. "Rationalizing rational expectations: Characterizations and tests," Quantitative Economics, Econometric Society, vol. 12(3), pages 817-842, July.
    4. Zhenting Sun & Kaspar Wuthrich, 2022. "Pairwise Valid Instruments," Papers 2203.08050, arXiv.org, revised Jan 2024.
    5. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.
    6. Xavier D'Haultfoeuille & Christophe Gaillac & Arnaud Maurel, 2018. "Rationalizing Rational Expectations? Tests and Deviations," NBER Working Papers 25274, National Bureau of Economic Research, Inc.
    7. Hongyi Jiang & Zhenting Sun, 2023. "Testing Partial Instrument Monotonicity," Papers 2308.08390, arXiv.org, revised Aug 2023.
    8. Julian Martinez-Iriarte, 2023. "Sensitivity Analysis in Unconditional Quantile Effects," Papers 2303.14298, arXiv.org, revised Jun 2023.
    9. Wang, Dewei & Tang, Chuan-Fa & Tebbs, Joshua M., 2020. "More powerful goodness-of-fit tests for uniform stochastic ordering," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.

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    More about this item

    Keywords

    Contact set; Density ratio ordering; Hadamard directional differentiability; Least concave majorant; Ordinal dominance curve;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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