Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học thế giới đề tài: Parameter expansion for estimation of reduced rank covariance matrices (Open Access publication) | Genet. Sel. Evol. 40 2008 3-24 INRA EDP Sciences 2008 DOI gse 2007032 Available online at Original article Parameter expansion for estimation of reduced rank covariance matrices Open Access publication Karin MEYER Animal Genetics and Breeding Unit University of New England Armidale NSW 2351 Australia Received 14 December 2006 accepted 25 June 2007 Abstract - Parameter expanded and standard expectation maximisation algorithms are described for reduced rank estimation of covariance matrices by restricted maximum likelihood fitting the leading principal components only. Convergence behaviour of these algorithms is examined for several examples and contrasted to that of the average information algorithm and implications for practical analyses are discussed. It is shown that expectation maximisation type algorithms are readily adapted to reduced rank estimation and converge reliably. However as is well known for the full rank case the convergence is linear and thus slow. Hence these algorithms are most useful in combination with the quadratically convergent average information algorithm in particular in the initial stages of an iterative solution scheme. restricted maximum likelihood reduced rank estimation algorithms expectation maximisation average information 1. INTRODUCTION Restricted maximum likelihood REML is one of the preferred methods for estimation of genetic parameters in animal breeding applications. Algorithms available to locate the maximum of the likelihood function differ in efficiency computational requirements ease of implementation and sensitivity to starting values in iterative schemes. The so-called average information algorithm has been found to be highly effective often converging in few rounds of iteration 40 . However there have been some albeit largely anecdotal observations of convergence problems for analyses with bad starting values many Corresponding author kmeyer@ AGBU is a joint venture .
