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.
Location Invariance, scale invariance. Pitmann’s estimators for location and scale parameters. Proof of the properties of M.L.E, Huzur Bazaar theorem
Consistent asymptotic normal (CAN) estimator, invariance property. Wilks likelihood ratio tests estimator,invariance of consistent asymptotic normal estimator
Asymptotic distribution of likelihood ratio statistic. Bartlett's test for homogeneity of variances.Generalized Neyman- Pearson lemma. Randomized tests.
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.
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.
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
Links:
[1] https://statistics.iisuniv.ac.in/courses/subjects/statistical-inference-ii
[2] https://statistics.iisuniv.ac.in/academic-year/2018-2019