Springer - Read

Problems 41
d. Under the conditions of part (c) show that the best linear unbiased estimator
of µ in terms of X1,...,Xn is ¯X 1
n (X1 + ··· + Xn). (ˆµ said to be an
unbiased estimator of µ if E ˆµ µ for all µ.)
e. Under the conditions of part (c) show that ¯X is the best linear predictor of
Xn+1 that is unbiased for µ.
f. If X1,X2,... is iid with E X2
i < ∞ and EXi µ, and if S0 0, Sn
X1 + ··· + Xn, n 1, 2,..., what is the minimum mean squared error
predictor of Sn+1 in terms of S1,...,Sn?
1.3. Show that a strictly stationary process with E(X2 i )