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Studentized permutation tests for non-i.i.d. hypotheses and the generalized Behrens-Fisher problem

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  • Janssen, Arnold

Abstract

It is shown that permutation tests based on studentized statistics are asymptotically exact of size [alpha] also under certain extended non-i.i.d. null hypotheses. To demonstrate the principle the results are applied to the generalized two-sample Behrens-Fisher problem for testing equality of the means under general non-parametric heterogeneous error distributions. Within this setting we propose a permutation version of the Welch test which is an extension of Pitman's two-sample permutation test. These results are special cases of a conditional central limit theorem for studentized permutation statistics which also applies to asymptotic power functions.

Suggested Citation

  • Janssen, Arnold, 1997. "Studentized permutation tests for non-i.i.d. hypotheses and the generalized Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 9-21, November.
    • Handle: RePEc:eee:stapro:v:36:y:1997:i:1:p:9-21
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    References listed on IDEAS

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    1. A. Janssen, 1989. "Local asymptotic normality for randomly censored models with applications to rank tests," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 43(2), pages 109-125, June.
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    Cited by:

    1. Steinke Ingo, 2004. "Locally asymptotically optimal tests in semiparametric generalized linear models in the 2-sample-problem," Statistics & Risk Modeling, De Gruyter, vol. 22(4/2004), pages 319-334, April.
    2. Friedrich, Sarah & Brunner, Edgar & Pauly, Markus, 2017. "Permuting longitudinal data in spite of the dependencies," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 255-265.
    3. Andreas Hagemann, 2019. "Permutation inference with a finite number of heterogeneous clusters," Papers 1907.01049, arXiv.org, revised Feb 2023.
    4. Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2018. "Inference Under Covariate-Adaptive Randomization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1784-1796, October.
    5. Hagemann, Andreas, 2019. "Placebo inference on treatment effects when the number of clusters is small," Journal of Econometrics, Elsevier, vol. 213(1), pages 190-209.
    6. Young, Alwyn, 2024. "Asymptotically robust permutation-based randomization confidence intervals for parametric OLS regression," LSE Research Online Documents on Economics 120933, London School of Economics and Political Science, LSE Library.
    7. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jun 2023.
    8. Dennis Dobler & Markus Pauly, 2018. "Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 639-658, September.
    9. Joseph Romano, 2009. "Discussion of ‘Parametric versus nonparametrics: two alternative methodologies’," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 419-424.
    10. Young, Alwyn, 2019. "Channeling Fisher: randomization tests and the statistical insignificance of seemingly significant experimental results," LSE Research Online Documents on Economics 101401, London School of Economics and Political Science, LSE Library.
    11. Cyrus J. DiCiccio & Joseph P. Romano, 2017. "Robust Permutation Tests For Correlation And Regression Coefficients," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1211-1220, July.
    12. Janssen Arnold & Völker Dominik, 2007. "Most powerful conditional tests," Statistics & Risk Modeling, De Gruyter, vol. 25(1/2007), pages 1-22, January.
    13. Zhao, Anqi & Ding, Peng, 2021. "Covariate-adjusted Fisher randomization tests for the average treatment effect," Journal of Econometrics, Elsevier, vol. 225(2), pages 278-294.
    14. Young, Alwyn, 2024. "Asymptotically robust permutation-based randomization confidence intervals for parametric OLS regression," European Economic Review, Elsevier, vol. 163(C).
    15. Brian D. Segal & Thomas Braun & Michael R. Elliott & Hui Jiang, 2018. "Fast approximation of small p†values in permutation tests by partitioning the permutations," Biometrics, The International Biometric Society, vol. 74(1), pages 196-206, March.
    16. Smaga, Łukasz, 2015. "Wald-type statistics using {2}-inverses for hypothesis testing in general factorial designs," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 215-220.
    17. Luis Alvarez & Bruno Ferman & Raoni Oliveira, 2022. "Randomization Inference Tests for Shift-Share Designs," Papers 2206.00999, arXiv.org.
    18. repec:sip:wpaper:12-026 is not listed on IDEAS
    19. Yuehao Bai & Joseph P. Romano & Azeem M. Shaikh, 2022. "Inference in Experiments With Matched Pairs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1726-1737, October.
    20. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.
    21. Chung, EunYi & Romano, Joseph P., 2016. "Multivariate and multiple permutation tests," Journal of Econometrics, Elsevier, vol. 193(1), pages 76-91.
    22. Ditzhaus, Marc & Smaga, Łukasz, 2022. "Permutation test for the multivariate coefficient of variation in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    23. Ditzhaus, Marc & Pauly, Markus, 2019. "Wild bootstrap logrank tests with broader power functions for testing superiority," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 1-11.
    24. Chung, EunYi & Olivares, Mauricio, 2021. "Permutation test for heterogeneous treatment effects with a nuisance parameter," Journal of Econometrics, Elsevier, vol. 225(2), pages 148-174.

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