Expected and Predicted Progress from Index Selection Involving Estimates of Population Parameters

Abstract

SUMMARY The nature of the index selection procedure when sample estimates are used in place of the true parameter values is considered. Approximate equations are developed for the low order moments of the joint distribution of the expected progress from selection for a particular calculated index and the predicted progress from this index. These equations involve the variances and covariances among the estimates used for index construction. Formulae are developed for these variances and covariances for paternal half-sib estimation. This joint distribution is also studied by a simulated sampling procedure. Numerical results for the two phases of the study are tabulated and studied for verification of the validity of the approximate equations and for assessment of the influence of the errors of estimation upon index selection procedures when estimates are obtained from paternal half-sib analyses of variance and covariance.