IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v116y2013icp1-13.html
   My bibliography  Save this article

Functional contour regression

Author

Listed:
  • Wang, Guochang
  • Lin, Nan
  • Zhang, Baoxue

Abstract

In this paper, we propose functional contour regression (FCR) for dimension reduction in the functional regression context. FCR achieves dimension reduction using the empirical directions on the functional predictor in contours defined on the response variable. It is more efficient than the functional variants of the sliced inverse regression (SIR) method by exploiting inter-slice information. A modified BIC is used to determine the dimensionality of the effective dimension reduction space. We prove that FCR is consistent in estimating the functional regression parameters, and simulations show that the estimates given by our FCR method provide better prediction accuracy than other existing methods such as functional sliced inverse regression, functional inverse regression and wavelet SIR. The merit of FCR is further demonstrated by two real data examples.

Suggested Citation

  • Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2013. "Functional contour regression," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 1-13.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:1-13
    DOI: 10.1016/j.jmva.2012.11.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12002643
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.11.005?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. Zhu, Lixing & Miao, Baiqi & Peng, Heng, 2006. "On Sliced Inverse Regression With High-Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 630-643, June.
    2. Baíllo, Amparo & Grané, Aurea, 2009. "Local linear regression for functional predictor and scalar response," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 102-111, January.
    3. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
    4. Jeng‐Min Chiou & Hans‐Georg Müller & Jane‐Ling Wang, 2003. "Functional quasi‐likelihood regression models with smooth random effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 405-423, May.
    5. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    6. James, Gareth M. & Silverman, Bernard W., 2005. "Functional Adaptive Model Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 565-576, 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. Linjuan Zheng & Beiting Liang & Guochang Wang, 2024. "Adaptive slicing for functional slice inverse regression," Statistical Papers, Springer, vol. 65(5), pages 3261-3284, July.
    2. Wang, Guochang & Zhou, Yan & Feng, Xiang-Nan & Zhang, Baoxue, 2015. "The hybrid method of FSIR and FSAVE for functional effective dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 64-77.
    3. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2014. "Functional k-means inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 172-182.

    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. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    2. Guochang Wang & Beiting Liang & Hansheng Wang & Baoxue Zhang & Baojian Xie, 2021. "Dimension reduction for functional regression with a binary response," Statistical Papers, Springer, vol. 62(1), pages 193-208, February.
    3. Li, Pai-Ling & Chiou, Jeng-Min & Shyr, Yu, 2017. "Functional data classification using covariate-adjusted subspace projection," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 21-34.
    4. Ciarleglio, Adam & Todd Ogden, R., 2016. "Wavelet-based scalar-on-function finite mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 86-96.
    5. Shuang Wu & Hans-Georg Müller, 2011. "Response-Adaptive Regression for Longitudinal Data," Biometrics, The International Biometric Society, vol. 67(3), pages 852-860, September.
    6. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2012. "Functional linear regression after spline transformation," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 587-601.
    7. Zhang, Xin & Wang, Chong & Wu, Yichao, 2018. "Functional envelope for model-free sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 37-50.
    8. Linjuan Zheng & Beiting Liang & Guochang Wang, 2024. "Adaptive slicing for functional slice inverse regression," Statistical Papers, Springer, vol. 65(5), pages 3261-3284, July.
    9. Chen, Lu-Hung & Jiang, Ci-Ren, 2018. "Sensible functional linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 39-52.
    10. Chen, Xuerong & Li, Haoqi & Liang, Hua & Lin, Huazhen, 2019. "Functional response regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 218-233.
    11. Chiou, Jeng-Min & Muller, Hans-Georg, 2007. "Diagnostics for functional regression via residual processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4849-4863, June.
    12. Wang, Qin & Yin, Xiangrong, 2011. "Estimation of inverse mean: An orthogonal series approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1656-1664, April.
    13. Coudret, R. & Girard, S. & Saracco, J., 2014. "A new sliced inverse regression method for multivariate response," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 285-299.
    14. Guochang Wang, 2017. "Dimension reduction in functional regression with categorical predictor," Computational Statistics, Springer, vol. 32(2), pages 585-609, June.
    15. Goldsmith, Jeff & Scheipl, Fabian, 2014. "Estimator selection and combination in scalar-on-function regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 362-372.
    16. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    17. Usset, Joseph & Staicu, Ana-Maria & Maity, Arnab, 2016. "Interaction models for functional regression," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 317-329.
    18. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
    19. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2014. "Functional k-means inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 172-182.
    20. Denis Agniel & Layla Parast, 2021. "Evaluation of longitudinal surrogate markers," Biometrics, The International Biometric Society, vol. 77(2), pages 477-489, June.

    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:116:y:2013:i:c:p:1-13. 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.