Prediction in Standard Linear Models.
Our usual linear model situation is that the YiS have zero covariance and identical variances. Thus, model (2) is satisfied with V = (]'2 I. A new observation yo would typically have zero covariance with the previous data, so VyO = O. It follows that 8* = 0 and the BLUP of yo is x~/J. This is just the BLUE of E(yo) = x~!3.