LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

SECOND SEMESTER – APRIL 2006

                                                          ST 2810 – SAMPLING THEORY

 

 

Date & Time : 24-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

Section A  (10 x 2 =20)

 

Answer ALL the questions. Each carries TWO marks.

1. Define : Midzuno sampling design
2. State the identity which relates sample size of a sampling design with its first order inclusion probabilities
3. Give the formula for unbiased estimator of under Warner’s RR
4. Define balanced systematic sampling
5. Mention the situations in which product and ratio estimators can be used instead of .
6. When do you recommend “Two phase sampling”?
7. Name an estimator which uses selection probabilities.
8. Give any two limitations of “Linear Systematic Sampling “
9. Name any one sampling-estimating strategy in which no unbiased estimator for variance of estimator can be found.
10. Write the variance of Yates corrected estimator under LSS when there is a linear trend in the population

Section B (5 x 8 = 40)

 

Answer any Five. Each carries Eight  marks.

11. Prove the following identities : and verify the same in the case of following sampling design

 

 

12. From a population containing N units a sample of n units is drawn using SRS and from the drawn sample a subsample of n’ units. Suggest an unbiased estimator for the population total based on the subsample and obtain its variance
13. Describe modified systematic sampling and show that under the model
14. Describe Desraj ordered estimator and obtain an unbiased estimator of

 

15. Explain proportional allocations (1) for a given cost (2) for a given sample size. Derive the variance of under the above cases assuming simple random sampling is used in all strata.

 

16. Explain Warner’s randomized response model in detail.

 

17. Define product estimator . Obtain an expression for its bias under simple random sampling and hence develop an unbiased estimator for the population total.
18. Derive the approximate mean square error of estimators in the class also obtain the minimum mean square error in the class.

 

Section C  (2 x 20 =40)

 

Answer any TWO. Each carries TWENTY marks

 

19. Define : Horvitz-Thompson estimator. Show that it is unbiased for the population total and derive its variance in Yates-Grundy form

 

20. Derive the first and second order inclusion probabilities under Midzuno sampling scheme and show that under this design the Yates-Grundy estimator is non-negative

 

21. Develop Yates corrected estimator under Linear Systematic Samping

 

22. Develop Hartley-Ross ratio type unbiased estimator under simple random sampling.

 

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