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August 1999 Asymptotic distribution of the reduced rank regression estimator under general conditions
T. W. Anderson
Ann. Statist. 27(4): 1141-1154 (August 1999). DOI: 10.1214/aos/1017938918

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.

Citation

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T. W. Anderson. "Asymptotic distribution of the reduced rank regression estimator under general conditions." Ann. Statist. 27 (4) 1141 - 1154, August 1999. https://doi.org/10.1214/aos/1017938918

Information

Published: August 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0961.62011
MathSciNet: MR1740118
Digital Object Identifier: 10.1214/aos/1017938918

Subjects:
Primary: 62E20, 62H10
Secondary: 62H12

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 4 • August 1999
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