Properties of BLUEs and BLUPs in Full vs. Small Linear Models with New Observations

Abstract

In this article we consider the partitioned linear model M12={y,X1β1+X2β2,V}, where μ = X1β1 + X2β2, and the corresponding small model M1={y,X1β1,V}, where μ1 = X1β1. These models are supplemented with the new unobservable random vector y∗, coming from y∗ = Kβ1 + ε∗, where the covariance matrix of y∗ is known as well as the cross-covariance matrix between y∗ and y. We focus on comparing the BLUEs of μ1 and μ, and BLUPs of y∗ and ε∗ under M12 and M1.