Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Restricted maximum likelihood estimation of covariances in sparse linear models | 3 Genet. Sei. Evol. 30 1998 3-26 Inra Elsevier Paris Original article Restricted maximum likelihood estimation of covariances in sparse linear models Arnold Neumaiera Eildert Groeneveldb a Institut fiir Mathematik Universităt Wien Strudlhofgasse 4 1090 Vienna Austria b Institut fiir Tierzucht und Tierverhalten Bundesforschungsanstalt fur Landwirtschaft Hõltystr. 10 31535 Neustadt Germany Received 16 December 1996 accepted 30 September 1997 Abstract - This paper discusses the restricted maximum likelihood REML approach for the estimation of covariance matrices in linear stochastic models as implemented in the current version of the VCE package for covariance component estimation in large animal breeding models. The main features are 1 the representation of the equations in an augmented form that simplifies the implementation 2 the parametrization of the covariance matrices by means of their Cholesky factors thus automatically ensuring their positive definiteness 3 explicit formulas for the gradients of the REML function for the case of large and sparse model equations with a large number of unknown covariance components and possibly incomplete data using the sparse inverse to obtain the gradients cheaply 4 use of model equations that make separate formation of the inverse of the numerator relationship matrix unnecessary. Many large scale breeding problems were solved with the new implementation among them an example with more than 250 000 normal equations and 55 covariance components taking 41 h CPU time on a Hewlett Packard 755. Inra Elsevier Paris restricted maximum likelihood variance component estimation missing data sparse inverse analytical gradients Resume Estimation par maximum de vraisemblance restreinte de covariance dans les systèmes linéaires peu denses. Ce papier discute de 1 approche par maximum de vraisemblance restreinte REML pour 1 estimation des matrices de covariances dans les modèles linéaires qu applique le logiciel VCE en génétique animale. Les
