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Robust Permutation Tests For Correlation And Regression Coefficients

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  • Cyrus J. DiCiccio
  • Joseph P. Romano

Abstract

Given a sample from a bivariate distribution, consider the problem of testing independence. A permutation test based on the sample correlation is known to be an exact level α test. However, when used to test the null hypothesis that the samples are uncorrelated, the permutation test can have rejection probability that is far from the nominal level. Further, the permutation test can have a large Type 3 (directional) error rate, whereby there can be a large probability that the permutation test rejects because the sample correlation is a large positive value, when in fact the true correlation is negative. It will be shown that studentizing the sample correlation leads to a permutation test which is exact under independence and asymptotically controls the probability of Type 1 (or Type 3) errors. These conclusions are based on our results describing the almost sure limiting behavior of the randomization distribution. We will also present asymptotically robust randomization tests for regression coefficients, including a result based on a modified procedure of Freedman and Lane. Simulations and empirical applications are included. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:519:p:1211-1220
    DOI: 10.1080/01621459.2016.1202117
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    References listed on IDEAS

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    1. Freedman, David & Lane, David, 1983. "A Nonstochastic Interpretation of Reported Significance Levels," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 292-298, October.
    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    3. Arnold Janssen, 2005. "Resampling student'st-type statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 507-529, September.
    4. 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.
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    Cited by:

    1. MacKinnon, James G. & Webb, Matthew D., 2020. "Randomization inference for difference-in-differences with few treated clusters," Journal of Econometrics, Elsevier, vol. 218(2), pages 435-450.
    2. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jul 2024.
    3. Young, Alwyn, 2024. "Asymptotically robust permutation-based randomization confidence intervals for parametric OLS regression," European Economic Review, Elsevier, vol. 163(C).
    4. 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.
    5. Joseph P. Romano & Marius A. Tirlea, 2022. "Permutation testing for dependence in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 781-807, September.
    6. Damian Clarke & Joseph P. Romano & Michael Wolf, 2020. "The Romano–Wolf multiple-hypothesis correction in Stata," Stata Journal, StataCorp LP, vol. 20(4), pages 812-843, December.
    7. Federico A. Bugni & Jia Li & Qiyuan Li, 2020. "Permutation-based tests for discontinuities in event studies," Papers 2007.09837, arXiv.org, revised Jul 2022.
    8. 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.
    9. 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.
    10. David M. Ritzwoller & Joseph P. Romano & Azeem M. Shaikh, 2024. "Randomization Inference: Theory and Applications," Papers 2406.09521, arXiv.org.
    11. Federico A. Bugni & Jia Li & Qiyuan Li, 2023. "Permutation‐based tests for discontinuities in event studies," Quantitative Economics, Econometric Society, vol. 14(1), pages 37-70, January.
    12. Nathaniel E. Helwig, 2022. "Robust Permutation Tests for Penalized Splines," Stats, MDPI, vol. 5(3), pages 1-18, September.
    13. Stefano Bonnini & Getnet Melak Assegie & Kamila Trzcinska, 2024. "Review about the Permutation Approach in Hypothesis Testing," Mathematics, MDPI, vol. 12(17), pages 1-29, August.

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