1
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
M.Sc.DEGREE EXAMINATION STATISTICS
SECONDSEMESTER APRIL 2018
17/16/ ST2814 PST2MC01- ESTIMATION THEORY
Date: 17-04-2018 Dept. No. Max. 100 Marks
Time: 01:00-04:00
SECTION A
Answer ALL the questions (10 x 2 20)
1. If X1 and X2 are then obtain the unbiased estimator of .
2. State the different approaches to identify UMVUE.
3. Define Minimum Variance Bound Estimator.
4. State Neyman Fisher Factorization Theorem
5. Let X1 and X2 be iid . Is 2 1 2 X X ancillary statistic?
6. Let X1, X2 be iidP(θ) θ>0. Show that X1+2X2 is not sufficient for θ.
7. Define completeness and bounded completeness.
8 . What is exponential class of family?
9. Suggest an MLEforP[X=0]in the caseofP(θ), θ>0.
10. Define CAN estimator.
SECTION B
Answer any FIVE questions x 8 40)
11. State and establish Uncorrelatedness approach of UMVUE.
12. Give an example for each of the following:
g U is empty g U is singleton.
13. State and establish Rao-Blackwell theorem.
14. Let X1,X2,…,Xn be a random sample from 2 N . Obtain the Cramer Rao lower bound
for estimating 2 .
15. Show that the family of 0 1 is complete.
16. Let X1,X2,…,Xn be a random sample of size n from 0. Obtain MVBE of θ and
suggest MVBE of where a and b are constants such that a 0 .
17. State and establish Basu's theorem.
18. Let X 0 . Assume that the prior distribution of is 0 . Find the
Baye's estimator if the loss function is absolute error.
2
SECTION C
Answer any TWO questions (2x 20 40)
19. If UMVUE exists for the parametric function then show that it must be essentially
unique.
Let n XXX,..., 1 2 be a random sample of size n from .
i. Obtain the information contained in the sample.
ii. Show that X is MVBE for estimating θ.
iii. Deduce that X is UMVUE for estimating θ.
20. Give an example of an estimator which is consistent but not CAN.
Let n XXX,..., 1 2 be a random sample of size n from a two parameter exponential
distribution . 0 R E Find MLE of and .
21. State and Prove Cramer-Rao inequality by stating its regularity conditions.
MLE is not consistent Support the statement with an example.
22. "Blind use of Jackknifed method" Illustrate with an example.
Write a short note on Bootstrap method.