IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i4p393-400.html
   My bibliography  Save this article

Dimension reduction via marginal high moments in regression

Author

Listed:
  • Yin, Xiangrong
  • Cook, R. Dennis

Abstract

Yin and Cook [2002. Dimension reduction for the conditional k-th moment in regression. J. Roy. Statist. Soc. B 64, 159-175] established a general equivalence between sliced inverse regression (sir) and a marginal moment method called Covk. In this note, we form a new marginal method called phdk and establish a general equivalence between sliced average variance estimation save, and Covk and phdk. We also show that in the population save is the most comprehensive method among all dimension reduction methods using the first two inverse moments. However, no similar relation was found for dimension reduction methods based on third inverse moments.

Suggested Citation

  • Yin, Xiangrong & Cook, R. Dennis, 2006. "Dimension reduction via marginal high moments in regression," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 393-400, February.
  • Handle: RePEc:eee:stapro:v:76:y:2006:i:4:p:393-400
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00311-1
    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. Xiangrong Yin, 2003. "Estimating central subspaces via inverse third moments," Biometrika, Biometrika Trust, vol. 90(1), pages 113-125, March.
    3. Ye Z. & Weiss R.E., 2003. "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 968-979, January.
    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. 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).
    2. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    3. 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.
    4. 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.
    5. Park, Yujin & Kim, Kyongwon & Yoo, Jae Keun, 2022. "On cross-distance selection algorithm for hybrid sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    6. 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.
    7. Dong, Yuexiao & Yu, Zhou, 2012. "Dimension reduction for the conditional kth moment via central solution space," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 207-218.
    8. 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.
    9. Wenjuan Li & Wenying Wang & Jingsi Chen & Weidong Rao, 2023. "Aggregate Kernel Inverse Regression Estimation," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    10. Iaci, Ross & Yin, Xiangrong & Zhu, Lixing, 2016. "The Dual Central Subspaces in dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 178-189.
    11. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    12. Melanie Birke & Sebastien Van Bellegem & Ingrid Van Keilegom, 2017. "Semi-parametric Estimation in a Single-index Model with Endogenous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 168-191, March.
    13. 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.
    14. da Silva, Murilo & Sriram, T.N. & Ke, Yuan, 2023. "Dimension reduction in time series under the presence of conditional heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    15. S. Yaser Samadi & Tharindu P. De Alwis, 2023. "Fourier Methods for Sufficient Dimension Reduction in Time Series," Papers 2312.02110, arXiv.org.
    16. 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.
    17. Lian, Heng & Li, Gaorong, 2014. "Series expansion for functional sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 150-165.
    18. Li, Weiyu & Patilea, Valentin, 2017. "A new minimum contrast approach for inference in single-index models," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 47-59.
    19. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    20. Zeng, Peng & Zhu, Yu, 2010. "An integral transform method for estimating the central mean and central subspaces," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 271-290, January.

    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:76:y:2006:i:4:p:393-400. 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.