IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v77y2007i8p817-821.html
   My bibliography  Save this article

A note on sufficient dimension reduction

Author

Listed:
  • Wen, Xuerong Meggie

Abstract

In this paper, we presented a theoretical result and then discussed possible applications of our result to SDR problems. In addition to providing insights into existing SDR methods when Y is univariate; our theorem also applies to multivariate responses, especially when the response takes the form of (Y,W), where Y is a continuous variable and W is categorical.

Suggested Citation

  • Wen, Xuerong Meggie, 2007. "A note on sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 817-821, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:8:p:817-821
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00014-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Xiangrong Yin & R. Dennis Cook, 2002. "Dimension reduction for the conditional kth moment in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 159-175, May.
    2. Nader Ebrahimi, 2003. "Identifiability and censored data," Biometrika, Biometrika Trust, vol. 90(3), pages 724-727, September.
    3. Jae Keun Yoo & R. Dennis Cook, 2007. "Optimal sufficient dimension reduction for the conditional mean in multivariate regression," Biometrika, Biometrika Trust, vol. 94(1), pages 231-242.
    4. R. Dennis Cook & Liqiang Ni, 2006. "Using intraslice covariances for improved estimation of the central subspace in regression," Biometrika, Biometrika Trust, vol. 93(1), pages 65-74, March.
    5. Cook, R. Dennis & Ni, Liqiang, 2005. "Sufficient Dimension Reduction via Inverse Regression: A Minimum Discrepancy Approach," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 410-428, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hilafu, Haileab & Wu, Wenbo, 2017. "Partial projective resampling method for dimension reduction: With applications to partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 1-14.
    2. Wen, Xuerong Meggie, 2010. "On sufficient dimension reduction for proportional censorship model with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1975-1982, August.

    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. Yoo, Jae Keun, 2008. "Sufficient dimension reduction for the conditional mean with a categorical predictor in multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1825-1839, September.
    2. Yoo, Jae Keun, 2009. "Partial moment-based sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 450-456, February.
    3. Lu Li & Kai Tan & Xuerong Meggie Wen & Zhou Yu, 2023. "Variable-dependent partial dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 521-541, June.
    4. Wei Sun & Lexin Li, 2012. "Multiple Loci Mapping via Model-free Variable Selection," Biometrics, The International Biometric Society, vol. 68(1), pages 12-22, March.
    5. 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).
    6. Li‐Ping Zhu & Li‐Xing Zhu, 2009. "On distribution‐weighted partial least squares with diverging number of highly correlated predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 525-548, April.
    7. Lian, Heng & Li, Gaorong, 2014. "Series expansion for functional sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 150-165.
    8. 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.
    9. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    10. Wenbin Lu & Lexin Li, 2011. "Sufficient Dimension Reduction for Censored Regressions," Biometrics, The International Biometric Society, vol. 67(2), pages 513-523, June.
    11. Portier, François & Delyon, Bernard, 2013. "Optimal transformation: A new approach for covering the central subspace," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 84-107.
    12. Howard D. Bondell & Lexin Li, 2009. "Shrinkage inverse regression estimation for model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 287-299, January.
    13. Wen, Xuerong Meggie, 2010. "On sufficient dimension reduction for proportional censorship model with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1975-1982, August.
    14. Zeng, Bilin & Yu, Zhou & Wen, Xuerong Meggie, 2015. "A note on cumulative mean estimation," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 322-327.
    15. Chen, Canyi & Xu, Wangli & Zhu, Liping, 2022. "Distributed estimation in heterogeneous reduced rank regression: With application to order determination in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    16. Yoo, Jae Keun, 2015. "A theoretical note on optimal sufficient dimension reduction with singularity," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 109-113.
    17. Hilafu, Haileab & Yin, Xiangrong, 2013. "Sufficient dimension reduction in multivariate regressions with categorical predictors," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 139-147.
    18. François Portier, 2016. "An Empirical Process View of Inverse Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 827-844, September.
    19. Yoo, Jae Keun & Cook, R. Dennis, 2008. "Response dimension reduction for the conditional mean in multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 334-343, December.
    20. Yoo, Jae Keun, 2008. "A novel moment-based sufficient dimension reduction approach in multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3843-3851, March.

    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:stapro:v:77:y:2007:i:8:p:817-821. 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.