As in Neyman and Scott (1948), let Yij ∼ normal(µi, σ2) (independent) for i = 1,...,n and j = 1,..., k. The maximum likelihood estimators are                                µˆ i = Y¯ i• and σˆ 2 = n...

As in Neyman and Scott (1948), let Yij ∼ normal(µi, σ2) (independent) for i = 1,...,n and j = 1,..., k. The maximum likelihood estimators are

                               µˆ i = Y¯ i• and σˆ 2 = n i=1 k j=1 (Yij − Y¯ i•)2 nk .

As n → ∞ with k fixed, show that σˆ 2 → [(k − 1)/k]σ2 and is not consistent for σ2.