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Properties of cyclic subspace regression

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

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.

Suggested Citation

  • Lang, Patrick & Gironella, Ann & Venema, Rienk, 2007. "Properties of cyclic subspace regression," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 625-637, March.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:625-637
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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. 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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