STAT 632-600
December 13, 2005
Final Exam
Instructions: Answer each question on the test paper provided. Circle the correct answer
on multiple choice questions. Be specific on short-answer questions. Each multiple choice
question is worth four points, and each of the other questions is worth 12 points. Have a
happy holiday!
1. A decision rule δis inadmissible if
(a) its Bayes risk is larger than that of the Bayes rule.
(b) there exist at least two decision rules having uniformly smaller risk than that of δ.
(c) there exists a rule δ1for which R(θ, δ1)≤R(θ, δ) for all θwith strict inequality for at
least one θ.
(d) there exists a rule δ1such that supθ∈ΘR(θ, δ1)<supθ∈ΘR(θ, δ).
(e) it is unable to stand up throughout an entire Aggie home game.
2. James-Stein theory is concerned mainly with
(a) admissibility of the sample mean as an estimator of a multivariate normal population
mean.
(b) admissibility of the sample variance as an estimator of population variance.
(c) large sample properties of maximum likelihood estimators.
(d) large sample properties of the mean of a posterior distribution.
(e) how to properly pour Pils vom Faβinto a German beer stein.
3. The observations Y1, . . . , Ynare a random sample from a normal distribution with mean
µand variance σ2, both of which are unknown. The prior distribution is
π(µ, σ) = 1
σφµµ
σ¶·2φ(σ)I(0,∞)(σ),
where φis the standard normal density and I(0,∞)is an indicator function. In this particular
problem, the prior πis
(a) a noninformative prior.
(b) a conjugate prior.
(c) an improper prior.
(d) none of the above.
(e) saddened at the passing of his buddy Richard Pryor.
1
