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Properties of cyclic subspace regression

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  • Lang, Patrick
  • Gironella, Ann
  • Venema, Rienk
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    Abstract

    Various properties of the regression vector produced by cyclic subspace regression with regard to the meancentered linear regression equation are put forth. In particular, the subspace associated with the creation of is shown to contain a basis that maximizes certain covariances with respect to , the orthogonal projection of onto a specific subspace of the range of X. This basis is constructed. Moreover, this paper shows how the maximum covariance values effect the . Several alternative representations of are also developed. These representations show that is a modified version of the l-factor principal components regression vector , with the modification occurring by a nonorthogonal projection. Additionally, these representations enable prediction properties associated with to be explicitly identified. Finally, methods for choosing factors are spelled out.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 3 (March)
    Pages: 625-637

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:625-637

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    Related research

    Keywords: Cyclic subspace regression Covariance maximization Regression vector representation Prediction Partial principal components Factor selection;

    References

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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. Lang, Patrick M. & Brenchley, Jason M. & Nieves, Reinaldo G. & Kalivas, John H., 1998. "Cyclic Subspace Regression," Journal of Multivariate Analysis, Elsevier, vol. 65(1), pages 58-70, April.
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