Statistical Inference-II

Paper Code: 
STT-321
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course aims at describing the advanced level topics in statistical methods and statistical inference. This course would prepare students to have a strong base in basic statistics that would help them in undertake basic and applied research in Statistics.

15.00
Unit I: 
UNIT I

Location Invariance, scale invariance. Pitmann’s estimators for location and scale parameters. Proof of the properties of M.L.E, Huzur Bazaar theorem

15.00
Unit II: 
UNIT II

Consistent asymptotic normal (CAN) estimator, invariance property. Wilks likelihood ratio tests estimator,invariance of consistent asymptotic normal estimator

15.00
Unit III: 
UNIT III

Asymptotic distribution of likelihood ratio statistic. Bartlett's test for homogeneity of variances.Generalized Neyman- Pearson lemma. Randomized tests.

15.00
Unit IV: 
UNIT IV

Uniformly most powerful tests for two-sided hypothesis. Unbiased tests. Uniformly most powerful unbiased tests. Generalised likelihood ratio test -mean and variance. Tests with Neyman’s Structures and its relation with complete family of distributions.

15.00
Unit V: 
UNIT V

Basic Elements of Statistical Decision Problem. Various inference problems viewed as decision problem. Randomization optimal decision rules. Bayes and minimax decision rule. Generalized Bayes rule.

Essential Readings: 

Books Recommended/Reference Books

1. Casela G & Berger RL. (2001): Statistical Inference. Duxbury Thompson Learning.

2. Conover WJ. (1980):  Practical Nonparametric Statistics. John Wiley.

3. Kiefer JC. (1987):  Introduction to Statistical Inference. Springer.

4. Lehmann EL. (1986) Theory of Point Estimation. John Wiley.

5. Wald A. (2004) Sequential Analysis. Dover Publ.

6. Cramer, H.(1946) : Mathematical methods of Statistics, Princeton University Press.

7. Goon and others.(1991): Outline of Statistical theory Vol-I, World Press.

8. Rao,C.R. (1973) : Linear Statistical inference and its applications, 2nd Ed,

John Wiley & Sons Inc.

9.  Gibbons,J.D. (1985): Non- Parametric Statistical Inference, McGraw-Hill.

10. Kendall, M.G. and Stuart, A. (1971): Advanced Theory of Statistic Vol. I and II,Charles Griffin.

11. Mood, Graybill and Boes. (1974): Introduction to the theory of Statistics 3rded, McGraw- Hill.

12. Hogg,R.V. and Craig,A.T.( (1971): Introduction to Mathematical Statistics, Princeton University Press.

13. Rao, C. R. (2002): Linear Statistical Inference and its Applications, Willey- Blackwell

14. Gibbons (1971): Non Parametric Inference, Chapman and Hall

15. Sidney and Siegal (1956):  Non Parametric for Behavioral science,Mcgraw-Hill Book Company

Academic Year: 
2018-2019
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