IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v149y2016icp81-91.html
   My bibliography  Save this article

On permutation tests for predictor contribution in sufficient dimension reduction

Author

Listed:
  • Dong, Yuexiao
  • Yang, Chaozheng
  • Yu, Zhou

Abstract

To test predictor contribution in a model-free fashion, marginal coordinate tests based on sliced inverse regression (SIR) and sliced average variance estimation (SAVE) have been studied in Cook (2004), and Shao et al. (2007) respectively. Estimating the null distributions of the test statistics is a critical step for such tests. We propose a novel permutation test approach to facilitate the marginal coordinate tests, which applies to existing tests based on SIR and SAVE, and can be readily extended to a new marginal coordinate test based on directional regression (Li and Wang, 2007).

Suggested Citation

  • Dong, Yuexiao & Yang, Chaozheng & Yu, Zhou, 2016. "On permutation tests for predictor contribution in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 81-91.
    • Handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:81-91
    DOI: 10.1016/j.jmva.2016.02.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16000634
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.02.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Bing & Wang, Shaoli, 2007. "On Directional Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 997-1008, September.
    2. T. Wang & X. Guo & L. Zhu & P. Xu, 2014. "Transformed sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 101(4), pages 815-829.
    3. Yongwu Shao & R. Dennis Cook & Sanford Weisberg, 2007. "Marginal tests with sliced average variance estimation," Biometrika, Biometrika Trust, vol. 94(2), pages 285-296.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yongtao Guan & Hansheng Wang, 2010. "Sufficient dimension reduction for spatial point processes directed by Gaussian random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 367-387, June.
    2. repec:jss:jstsof:39:i03 is not listed on IDEAS
    3. Zhou Yu & Yuexiao Dong & Li-Xing Zhu, 2016. "Trace Pursuit: A General Framework for Model-Free Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 813-821, April.
    4. Stephen Babos & Andreas Artemiou, 2020. "Sliced inverse median difference regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 937-954, December.
    5. Dong, Yuexiao & Li, Zeda, 2024. "A note on marginal coordinate test in sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 204(C).
    6. Alothman, Ahmad & Dong, Yuexiao & Artemiou, Andreas, 2018. "On dual model-free variable selection with two groups of variables," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 366-377.
    7. Yu, Zhou & Dong, Yuexiao & Guo, Ranwei, 2013. "On determining the structural dimension via directional regression," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 987-992.
    8. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 130-142, January.
    9. Artemiou, Andreas & Tian, Lipu, 2015. "Using sliced inverse mean difference for sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 184-190.
    10. Yu, Zhou & Zhu, Lixing & Wen, Xuerong Meggie, 2012. "On model-free conditional coordinate tests for regressions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 61-72.
    11. Li, Junlan & Wang, Tao, 2021. "Dimension reduction in binary response regression: A joint modeling approach," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    12. Hino, Hideitsu & Wakayama, Keigo & Murata, Noboru, 2013. "Entropy-based sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 105-114.
    13. Scrucca, Luca, 2011. "Model-based SIR for dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3010-3026, November.
    14. Szretter Noste, María Eugenia, 2019. "Using DAGs to identify the sufficient dimension reduction in the Principal Fitted Components model," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 317-320.
    15. Stephen Babos & Andreas Artemiou, 2021. "Cumulative Median Estimation for Sufficient Dimension Reduction," Stats, MDPI, vol. 4(1), pages 1-8, February.
    16. Hung Hung & Su‐Yun Huang, 2019. "Sufficient dimension reduction via random‐partitions for the large‐p‐small‐n problem," Biometrics, The International Biometric Society, vol. 75(1), pages 245-255, March.
    17. repec:wyi:journl:002176 is not listed on IDEAS
    18. Wang, Tao & Xu, Pei-Rong & Zhu, Li-Xing, 2012. "Non-convex penalized estimation in high-dimensional models with single-index structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 221-235.
    19. Wang, Pei & Yin, Xiangrong & Yuan, Qingcong & Kryscio, Richard, 2021. "Feature filter for estimating central mean subspace and its sparse solution," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    20. Charles Lindsey & Simon Sheather & Joseph McKean, 2014. "Using sliced mean variance–covariance inverse regression for classification and dimension reduction," Computational Statistics, Springer, vol. 29(3), pages 769-798, June.
    21. Ondřej Šedivý & Antti Penttinen, 2014. "Intensity estimation for inhomogeneous Gibbs point process with covariates-dependent chemical activity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(3), pages 225-249, August.
    22. Hayley Randall & Andreas Artemiou & Xingye Qiao, 2021. "Sufficient dimension reduction based on distance‐weighted discrimination," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1186-1211, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:81-91. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.