The Annals of Statistics

Maximum Likelihood Estimation of a Set of Covariance Matrices Under Lowner Order Restrictions with Applications to Balanced Multivariate Variance Components Models

James A. Calvin and Richard L. Dykstra

Full-text: Open access

Abstract

The problem of maximum likelihood estimation of Lowner ordered covariance matrices is considered. It is shown that a dual formulation of this problem is tractable and important in its own right. The interplay between the primal and dual problems suggests a general algorithm for computing the solutions to these problems. This algorithm has application to some estimation problems in balanced multivariate variance components models. The speed of convergence is also discussed for the variance components models.

Article information

Source
Ann. Statist., Volume 19, Number 2 (1991), 850-869.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348124

Digital Object Identifier
doi:10.1214/aos/1176348124

Mathematical Reviews number (MathSciNet)
MR1105848

Zentralblatt MATH identifier
0761.62068

JSTOR
links.jstor.org

Subjects
Primary: 62H12: Estimation
Secondary: 62J10: Analysis of variance and covariance

Keywords
Isotonic regression Wishart density Fenchel duality multivariate linear model restricted maximum likelihood estimation REML variance components models least squares estimation

Citation

Calvin, James A.; Dykstra, Richard L. Maximum Likelihood Estimation of a Set of Covariance Matrices Under Lowner Order Restrictions with Applications to Balanced Multivariate Variance Components Models. Ann. Statist. 19 (1991), no. 2, 850--869. doi:10.1214/aos/1176348124. https://projecteuclid.org/euclid.aos/1176348124


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