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Showing papers by "T. W. Anderson published in 1999"


Journal ArticleDOI
TL;DR: In this paper, the asymptotic distribution of the sample canonical correlations and coefficients of the canonical variates is obtained when the nonzero population canonical correlations are distinct and sampling is from the normal distribution.

69 citations


Journal ArticleDOI
TL;DR: In this paper, the asymptotic distribution of the reduced rank regression estimator of the first $k$ canonical variates of the regression model is compared with that of the non-canonical variates.
Abstract: In the regression model $\mathbf{Y} = \eta + \mathbf{BX} + \mathbf{Z}$ with $\mathbf{Z}$ unobserved, $\mathscr{E}\mathbf{Z} = \mathbf{0}$ and $\mathscr{E}\mathbf{ZZ}' = \mathbf{\Sigma}_{ZZ}$, the least squares estimator of $\mathbf{B}$ is $\hat{\mathbf{B}} = \mathbf{S}_{YX}\mathbf{S}_{XX}^{-1}$. If the rank of $\mathbf{B}$ is known to be $k$ less than the dimensions of $\mathbf{Y}$ and $\mathbf{X}$, the reduced rank regression estimator of $\mathbf{B}$, say $\mathbf{B}_k$, depends on the first $k$ canonical variates of $\mathbf{Y}$ and $\mathbf{X}$. The asymptotic distribution of $\hat{\mathbf{B}}_k$ is obtained and compared with the asymptotic distribution of $\hat{\mathbf{B}}$. The advantage of $\hat{\mathbf{B}}_k$ is characterized.

66 citations