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Functional contour regression

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    Cited by:

    1. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2014. "Functional k-means inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 172-182.
    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.

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