Estimation of a covariance matrix with zeros

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call iterative conditional fitting, for computing the maximum likelihood estimate of the constrained covariance matrix, unde...

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Bibliographic Details
Published in:Biometrika 2007-03, Vol.94 (1), p.199-216
Main Authors: Chaudhuri, Sanjay, Drton, Mathias, Richardson, Thomas S.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Applications
Biology, psychology, social sciences
Covariance
Covariance graph
Covariance matrices
Empirical likelihood
Estimating techniques
Estimators
Exact sciences and technology
Gaussian distributions
Gene expression
Graphical model
Linear and multilinear algebra, matrix theory
Marginal independence
Mathematical functions
Mathematical vectors
Mathematics
Matrix
Maximum likelihood estimation
Maximum likelihood estimators
Multivariate analysis
Multivariate normal distribution
Normal distribution
Probability and statistics
Random variables
Sample size
Sciences and techniques of general use
Statistics
Studies
Variance analysis
Vertices
Citations: Items that cite this one
Online Access:Get full text
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Description
Summary:We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call iterative conditional fitting, for computing the maximum likelihood estimate of the constrained covariance matrix, under the assumption of multivariate normality. In contrast to previous approaches, this algorithm has guaranteed convergence properties. Dropping the assumption of multivariate normality, we show how to estimate the covariance matrix in an empirical likelihood approach. These approaches are then compared via simulation and on an example of gene expression.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asm007