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  • Review
  • Open Access

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

Genetics Selection Evolution200840:3

https://doi.org/10.1186/1297-9686-40-1-3

  • Received: 14 December 2006
  • Accepted: 25 June 2007
  • Published:

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.

Keywords

  • restricted maximum likelihood
  • reduced rank estimation
  • algorithms
  • expectation maximisation
  • average information

(To access full article, please see PDF)

Authors’ Affiliations

(1)
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

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