THE UNIVERSITY OF NEW SOUTH WALES
DEPARTMENT OF STATISTICS
Additional Exercises for MATH5905, Statistical Inference
Part two: Data reduction. Sufficient statistics. Classical estimation
Sufficiency
1. Use the factorization criterion to find a sufficient s
THE UNIVERSITY OF NEW SOUTH WALES
DEPARTMENT OF STATISTICS
Additional Exercises for MATH5905, Statistical Inference
Part one: Decision theory. Bayes and minimax rules
1. Suppose d1 , d2 , d3 and d4 are nonrandomized
i
R(1 , di )
R(2 , di )
decision
1 2
0
THE UNIVERSITY OF NEW SOUTH WALES
DEPARTMENT OF STATISTICS
Solutions to selected exercises for MATH5905, Statistical Inference
Part two: Data reduction. Sufficient statistics. Classical estimation
Pn
Question 1 a) Denoting T = i=1 Xi , you can factorise L
THE UNIVERSITY OF NEW SOUTH WALES
DEPARTMENT OF STATISTICS
Solutions to selected exercises for MATH5905, Statistical Inference
Part one: Decision theory. Bayes and minimax rules
Question 1 Answers: Please draw carefully the graph of the risk set before do
MATH5905 Statistical Inference
Assignment Two
1 Problem 1
1.1 a
: :13? I(Uy(1)(9)
2; y? Imam)
This is independent of 6 if 22(1) 2 y). This is Lehlnann-Sclleffcs method and T = X) is a
minimal sufficient statistic for 9. x
5 1.2 b
32
=Eif9329el