Best Linear Unbiased Prediction: Introduction

Abstract

The derivation of Best Linear Prediction (Chapter 4) and selection index theory (Chapter 9) assumed that both the first and second moments of the joint distribution of g and y were known constants. That is, the means, variances and covariances are assumed known. In practice, these are never known exactly and estimates must be used (as was done in Chapters 4-10). This means that in all applications of BLP, the predicted breeding values are approximations to BLP. To the extent that the estimated first and second moments closely approximate the true moments, the predicted breeding values closely approximate best linear predictions (see Chapter 7).