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Nonparametric tests for and against likelihood ratio ordering in the two-sample problem

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  • Christopher A. Carolan
  • Joshua M. Tebbs

Abstract

We derive nonparametric procedures for testing for and against likelihood ratio ordering in the two-population setting with continuous distributions. We account for this ordering by examining the least concave majorant of the ordinal dominance curve formed from the nonparametric maximum likelihood estimators of the continuous distribution functions F and G. In particular, we focus on testing equality of F and G versus likelihood ratio ordering and testing for a violation of likelihood ratio ordering. For both testing problems, we propose area-based and sup-norm-based test statistics, derive appropriate limiting distributions, and provide simulation results that characterise the performance of our procedures. We illustrate our methods using data from a controlled experiment involving the effects of radiation on mice. Copyright 2005, Oxford University Press.

Suggested Citation

  • Christopher A. Carolan & Joshua M. Tebbs, 2005. "Nonparametric tests for and against likelihood ratio ordering in the two-sample problem," Biometrika, Biometrika Trust, vol. 92(1), pages 159-171, March.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:1:p:159-171
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    File URL: http://hdl.handle.net/10.1093/biomet/92.1.159
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    Citations

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    Cited by:

    1. Beare, Brendan K. & Moon, Jong-Myun, 2012. "Testing the concavity of an ordinaldominance curve," University of California at San Diego, Economics Working Paper Series qt6qg1f8ms, Department of Economics, UC San Diego.
    2. Brendan K. Beare & Lawrence D. W. Schmidt, 2016. "An Empirical Test of Pricing Kernel Monotonicity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 338-356, March.
    3. 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.
    4. Graham Elliott & Nikolay Kudrin & Kaspar Wüthrich, 2022. "Detecting p‐Hacking," Econometrica, Econometric Society, vol. 90(2), pages 887-906, March.
    5. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    6. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.
    7. Wei Zhang & Larry L. Tang & Qizhai Li & Aiyi Liu & Mei‐Ling Ting Lee, 2020. "Order‐restricted inference for clustered ROC data with application to fingerprint matching accuracy," Biometrics, The International Biometric Society, vol. 76(3), pages 863-873, September.
    8. Graham Elliott & Nikolay Kudrin & Kaspar Wuthrich, 2022. "The Power of Tests for Detecting $p$-Hacking," Papers 2205.07950, arXiv.org, revised Apr 2024.
    9. OrI Davidov & Konstantinos Fokianos & George Iliopoulos, 2014. "Semiparametric Inference for the Two-way Layout Under Order Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 622-638, September.
    10. 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).
    11. Seo, Juwon, 2018. "Tests of stochastic monotonicity with improved power," Journal of Econometrics, Elsevier, vol. 207(1), pages 53-70.

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