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