BLUPs: As discussed in Section 23.8, show that for the random-effects oneway ANOVA model, Y ij = β 1 + δ 1i + ε ij , the weights w i = n i minimize the variance of the estimator and thus that this...

BLUPs: As discussed in Section 23.8, show that for the random-effects oneway ANOVA model, Y_ij
= β₁
+ δ_1i
+ ε_ij, the weights w_i
= n_i
minimize the variance of the estimator

and thus that this choice provides the best linear unbiased estimator (BLUE) of β₁. Then explain why

is the best linear unbiased predictor (BLUP) of δ_1i.