The Annals of Statistics

Asymptotic distribution of the reduced rank regression estimator under general conditions

T. W. Anderson

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 27, Number 4 (1999), 1141-1154.

Dates
First available in Project Euclid: 4 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1017938918

Digital Object Identifier
doi:10.1214/aos/1017938918

Mathematical Reviews number (MathSciNet)
MR1740118

Zentralblatt MATH identifier
0961.62011

Subjects
Primary: 62H10: Distribution of statistics 62E20: Asymptotic distribution theory
Secondary: 62H12: Estimation

Keywords
Canonical variates reduced rank regression maximum likelihood estimators

Citation

Anderson, T. W. Asymptotic distribution of the reduced rank regression estimator under general conditions. Ann. Statist. 27 (1999), no. 4, 1141--1154. doi:10.1214/aos/1017938918. https://projecteuclid.org/euclid.aos/1017938918


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  • STANFORD, CALIFORNIA 94305-4065 E-MAIL: twa@stat.stanford.edu