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Some insights into continuum regression and its asymptotic properties

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  • Xin Chen
  • R. Dennis Cook

Abstract

Continuum regression encompasses ordinary least squares regression, partial least squares regression and principal component regression under the same umbrella using a nonnegative parameter Gamma. However, there seems to be no literature discussing the asymptotic properties for arbitrary continuum regression parameter Gamma. This article establishes a relation between continuum regression and sufficient dimension reduction and studies the asymptotic properties of continuum regression for arbitrary Gamma under inverse regression models. Theoretical and simulation results show that the continuum seems unnecessary when the conditional distribution of the predictors given the response follows the multivariate normal distribution. Copyright 2010, Oxford University Press.

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  • Xin Chen & R. Dennis Cook, 2010. "Some insights into continuum regression and its asymptotic properties," Biometrika, Biometrika Trust, vol. 97(4), pages 985-989.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:4:p:985-989
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    File URL: http://hdl.handle.net/10.1093/biomet/asq024
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    Cited by:

    1. Chen, Xin & Zhu, Li-Ping, 2015. "Connecting continuum regression with sufficient dimension reduction," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 44-49.
    2. Zhou, Zhiyang, 2019. "Functional continuum regression," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 328-346.

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