Abstract
SUMMARY: The extraction of sire proofs from non-orthogonal field data of the type met with in cattle A.I. populations presents special problems.A weighted least squares procedure for the estimation of sire effects from data of this kind, cross-classified by sire and herd, is described. Expected Breeding Values computed from these estimates have certain optimum properties. The standard errors of the estimates of the Expected Breeding Values are derived. The method makes it possible to classify the sires into groups before the proofs are computed. This sub-division of the stud could be useful in young sire evaluation and in measuring genetic trends in the proven stud. The computations are readily programmed for a computer, and the assumptions involved in the use of the method are particularly well suited to A.I. progeny field data, especially where an annual draft of young sires is being tested. A worked example is given.

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