Exercise 9.6.3 The missing value procedure that consists of analyzing the model (Y Z) = X +e

Exercise 9.6.3 The missing value procedure that consists of analyzing the model

(Y −Zγˆ) = Xβ +e has been shown to give the correct SSE and BLUEs; however, sums of squares explained by the model are biased upwards. For a randomized complete block design with a treatments and b blocks and the observation in the c,d cell missing, show that the correct mean square for treatments is the naive (biased) mean square treatments minus [y·d −(a−1) ˆ ycd ]2/a(a−1)2, where y·d is the sum of all actual observations in block

d, and ˆ ycd is the pseudo-observation (the nonzero element of Zγˆ).