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Connecting continuum regression with sufficient dimension reduction

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  • Chen, Xin
  • Zhu, Li-Ping

Abstract

Chen and Cook (2010) showed that the classical continuum regression with a nonzero tuning parameter may fail to produce a consistent estimator. In this article we show that the continuum regression with either slightly modified constraints or the tuning parameter being zero can estimate the central subspace consistently. We further provide a general class of continuum regression and connect it with sufficient dimension regression.

Suggested Citation

  • Chen, Xin & Zhu, Li-Ping, 2015. "Connecting continuum regression with sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 44-49.
    • Handle: RePEc:eee:stapro:v:98:y:2015:i:c:p:44-49
    DOI: 10.1016/j.spl.2014.12.007
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    References listed on IDEAS

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    1. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    2. Zhu, Li-Ping & Zhu, Li-Xing & Feng, Zheng-Hui, 2010. "Dimension Reduction in Regressions Through Cumulative Slicing Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1455-1466.
    3. Xin Chen & R. Dennis Cook, 2010. "Some insights into continuum regression and its asymptotic properties," Biometrika, Biometrika Trust, vol. 97(4), pages 985-989.
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    Cited by:

    1. Zhou, Zhiyang, 2019. "Functional continuum regression," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 328-346.

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