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


  • Janssen, Arnold


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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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Chung, EunYi & Romano, Joseph P., 2016. "Multivariate and multiple permutation tests," Journal of Econometrics, Elsevier, vol. 193(1), pages 76-91.
    6. Janssen Arnold & Völker Dominik, 2007. "Most powerful conditional tests," Statistics & Risk Modeling, De Gruyter, vol. 25(1/2007), pages 1-22, January.
    7. Federico A. Bugni & Ivan A. Canay & Azeem M. Shaikh, 2015. "Inference under covariate-adaptive randomization," CeMMAP working papers CWP45/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Joseph Romano, 2009. "Discussion of ‘Parametric versus nonparametrics: two alternative methodologies’," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 419-424.
    9. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105,
    10. 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.
    11. repec:sip:wpaper:12-026 is not listed on IDEAS
    12. 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.
    13. 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.
    14. Andreas Hagemann, 2019. "Permutation inference with a finite number of heterogeneous clusters," Papers 1907.01049,
    15. Azeem M. Shaikh, 2019. "Inference in Experiments with Matched Pairs," CeMMAP working papers CWP19/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. 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.


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