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Nonparametric Tests Of Density Ratio Ordering

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  • Beare, Brendan K.
  • Moon, Jong-Myun

Abstract

We study a family of nonparametric tests of density ratio ordering between two continuous probability distributions on the real line. Density ratio ordering is satisfied when the two distributions admit a nonincreasing density ratio. Equivalently, density ratio ordering is satisfied when the ordinal dominance curve associated with the two distributions is concave. To test this property, we consider statistics based on the Lp-distance between an empirical ordinal dominance curve and its least concave majorant. We derive the limit distribution of these statistics when density ratio ordering is satisfied. Further, we establish that, when 1 ≤ p ≤ 2, the limit distribution is stochastically largest when the two distributions are equal. When 2

Suggested Citation

  • Beare, Brendan K. & Moon, Jong-Myun, 2015. "Nonparametric Tests Of Density Ratio Ordering," Econometric Theory, Cambridge University Press, vol. 31(3), pages 471-492, June.
    • Handle: RePEc:cup:etheor:v:31:y:2015:i:03:p:471-492_00
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    Cited by:

    1. Abel Brodeur, Nikolai M. Cook, Jonathan S. Hartley, Anthony Heyes, 2022. "Do Pre-Registration and Pre-analysis Plans Reduce p-Hacking and Publication Bias?," LCERPA Working Papers am0132, Laurier Centre for Economic Research and Policy Analysis.
    2. Sangita Kulathinal & Isha Dewan, 2023. "Weighted U-statistics for likelihood-ratio ordering of bivariate data," Statistical Papers, Springer, vol. 64(2), pages 705-735, April.
    3. Graham Elliott & Nikolay Kudrin & Kaspar Wüthrich, 2022. "Detecting p‐Hacking," Econometrica, Econometric Society, vol. 90(2), pages 887-906, March.
    4. Pedro H. C. Sant’Anna, 2021. "Nonparametric Tests for Treatment Effect Heterogeneity With Duration Outcomes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 816-832, July.
    5. 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.
    6. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    7. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    8. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.
    9. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    10. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle in forward looking data," Review of Derivatives Research, Springer, vol. 21(3), pages 253-276, October.
    11. Xi Chen & Victor Chernozhukov & Iv'an Fern'andez-Val & Scott Kostyshak & Ye Luo, 2018. "Shape-Enforcing Operators for Point and Interval Estimators," Papers 1809.01038, arXiv.org, revised Feb 2021.
    12. Abel Brodeur & Nikolai M. Cook & Jonathan S. Hartley & Anthony Heyes, 2024. "Do Preregistration and Preanalysis Plans Reduce p-Hacking and Publication Bias? Evidence from 15,992 Test Statistics and Suggestions for Improvement," Journal of Political Economy Microeconomics, University of Chicago Press, vol. 2(3), pages 527-561.
    13. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.
    14. Graham Elliott & Nikolay Kudrin & Kaspar Wuthrich, 2022. "The Power of Tests for Detecting $p$-Hacking," Papers 2205.07950, arXiv.org, revised Apr 2024.
    15. 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).
    16. Seo, Juwon, 2018. "Tests of stochastic monotonicity with improved power," Journal of Econometrics, Elsevier, vol. 207(1), pages 53-70.

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