The Annals of Statistics

Estimation of Parameter Matrices and Eigenvalues in MANOVA and Canonical Correlation Analysis

Pui Lam Leung and Robb J. Muirhead

Full-text: Open access

Abstract

We consider the problem of estimating parameter matrices which occur in the noncentral Wishart, noncentral multivariate $F$ and canonical correlations distributions. A decision-theoretic approach is taken with squared error as the loss function. In these three settings the eigenvalues of the parameter matrices are of primary interest. Sensible estimates of these are obtained by restricting attention to orthogonally invariant estimates of the parameter matrices, whose eigenvalues are functions only of sample eigenvalues.

Article information

Source
Ann. Statist., Volume 15, Number 4 (1987), 1651-1666.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350616

Digital Object Identifier
doi:10.1214/aos/1176350616

Mathematical Reviews number (MathSciNet)
MR913580

Zentralblatt MATH identifier
0629.62059

JSTOR
links.jstor.org

Subjects
Primary: 62H12: Estimation

Keywords
Estimation of parameter matrices and eigenvalues noncentral Wishart distribution dominance MANOVA canonical correlations

Citation

Leung, Pui Lam; Muirhead, Robb J. Estimation of Parameter Matrices and Eigenvalues in MANOVA and Canonical Correlation Analysis. Ann. Statist. 15 (1987), no. 4, 1651--1666. doi:10.1214/aos/1176350616. https://projecteuclid.org/euclid.aos/1176350616


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