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Estimation of Variance Components Under a Selection Model

Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario, Canada N1G 2W1

ABSTRACT

A procedure for the estimation of variance components free of bias due to selection on a random vector correlated with the observation vector is presented. The estimators are based on restricted maximum likelihood methods for unselected situations and expectations derived under the pretense that a priori values are equal to true values. In the case of no selection, the formulas reduce to the usual formulas for restricted maximum likelihood. The properties of estimators under a selection model were not derived, because after selection, multivariate normality may no longer be assumed. Applications to particular selection problems in dairy cattle are discussed.

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