3.6 (a) If X1,...,Xn are iid with density f (x), show that the MRE estimator against squared...

3.6

(a) If X1,...,Xn are iid with density f (x−θ), show that the MRE estimator against squared error loss [the Pitman estimator of (3.1.28)] is the Bayes estimator against right-invariant Haar measure.

(b) If X1,...,Xn are iid with density 1/τf [(x − µ)/τ ], show that:

(i) Under squared error loss, the Pitman estimator of (3.1.28) is the Bayes estimator against right-invariant Haar measure.

(ii) Under the loss (3.3.17), the Pitman estimator of (3.3.19) is the Bayes estimator against right-invariant Haar measure.