Open Access
Genet. Sel. Evol.
Volume 40, Number 1, January-February 2008
Page(s) 3 - 24
Published online 21 December 2007
Genet. Sel. Evol. 40 (2008) 3-24
DOI: 10.1051/gse:2007032

Parameter expansion for estimation of reduced rank covariance matrices (Open Access publication)

Karin Meyer

Animal Genetics and Breeding Unit (AGBU is a joint venture between the NSW Department of Primary Industries and the University of New England.) , University of New England, Armidale NSW 2351, Australia

(Received 14 December 2006; accepted 25 June 2007; published online 21 December 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.

Key words: restricted maximum likelihood / reduced rank estimation / algorithms / expectation maximisation / average information

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© INRA, EDP Sciences 2008