IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v94y2007i3p615-625.html
   My bibliography  Save this article

Partial inverse regression

Author

Listed:
  • Lexin Li
  • R. Dennis Cook
  • Chih-Ling Tsai

Abstract

In regression with a vector of quantitative predictors, sufficient dimension reduction methods can effectively reduce the predictor dimension, while preserving full regression information and assuming no parametric model. However, all current reduction methods require the sample size n to be greater than the number of predictors p. It is well known that partial least squares can deal with problems with n < p. We first establish a link between partial least squares and sufficient dimension reduction. Motivated by this link, we then propose a new dimension reduction method, entitled partial inverse regression. We show that its sample estimator is consistent, and that its performance is similar to or superior to partial least squares when n < p, especially when the regression model is nonlinear or heteroscedastic. An example involving the spectroscopy analysis of biscuit dough is also given. Copyright 2007, Oxford University Press.

Suggested Citation

  • Lexin Li & R. Dennis Cook & Chih-Ling Tsai, 2007. "Partial inverse regression," Biometrika, Biometrika Trust, vol. 94(3), pages 615-625.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:3:p:615-625
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asm043
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    Citations

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


    Cited by:

    1. Qin Wang & Yuan Xue, 2023. "A structured covariance ensemble for sufficient dimension reduction," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 777-800, September.
    2. Bousebata, Meryem & Enjolras, Geoffroy & Girard, Stéphane, 2023. "Extreme partial least-squares," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    3. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. 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.
    5. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    6. Zifang Guo & Lexin Li & Wenbin Lu & Bing Li, 2015. "Groupwise Dimension Reduction via Envelope Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1515-1527, December.
    7. Prasad Naik & Michel Wedel & Lynd Bacon & Anand Bodapati & Eric Bradlow & Wagner Kamakura & Jeffrey Kreulen & Peter Lenk & David Madigan & Alan Montgomery, 2008. "Challenges and opportunities in high-dimensional choice data analyses," Marketing Letters, Springer, vol. 19(3), pages 201-213, December.
    8. Wenjuan Li & Wenying Wang & Jingsi Chen & Weidong Rao, 2023. "Aggregate Kernel Inverse Regression Estimation," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    9. Oliver J. Rutz & Michael Trusov & Randolph E. Bucklin, 2011. "Modeling Indirect Effects of Paid Search Advertising: Which Keywords Lead to More Future Visits?," Marketing Science, INFORMS, vol. 30(4), pages 646-665, July.
    10. Ghosh, Debashis, 2011. "Propensity score modelling in observational studies using dimension reduction methods," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 813-820, July.
    11. Li, Lexin, 2009. "Exploiting predictor domain information in sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2665-2672, May.
    12. Jain Yashita & Ding Shanshan & Qiu Jing, 2019. "Sliced inverse regression for integrative multi-omics data analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(1), pages 1-13, February.
    13. Cook, R. Dennis & Forzani, Liliana & Liu, Lan, 2023. "Partial least squares for simultaneous reduction of response and predictor vectors in regression," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

    More about this item

    Statistics

    Access and download statistics

    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:oup:biomet:v:94:y:2007:i:3:p:615-625. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.