2005/08/15 by Sanjay Chaudhuri, Subhajyoti Chaudhuri, Mathias Drton +1 · 126 citations
Computer Science · Mathematics · #Applied mathematics #Asymptotic distribution #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #CMA-ES #Covariance #Covariance function #Covariance intersection #Covariance matrix #Estimation of covariance matrices #Estimator #Mathematics #Matrix t-distribution #Multivariate normal distribution #Multivariate random variable #Multivariate statistics #Random variable #Rational quadratic covariance function #Scatter matrix #Statistical Methods and Inference #Statistics #math.ST #msc:62G05 #msc:62H12 #stat.TH
paper · pdf · doi:10.1093/biomet/asm007
published in Biometrika 94(1), 199-216 (Oxford University Press) · 25 pages
arxiv created 2005/08/15 · openalex publication_date 2007/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.