Coming soon
Statistical Inference-I
This course lays the foundation of Statistical Inference. The students would be taught the problems related to point and confidence interval estimation and testing of hypothesis. They would also be given the concepts of nonparametric and sequential test procedures.
Point estimation, criteria of a good estimator: unbiasedness, consistency, efficiency and sufficiency. Fisher Neyman factorization theorem, Cramer-Rao inequality, Bhattacharyra Bounds, Rao-Blackwell theorem, Completeness and Lehmann-Scheffe theorem, minimal sufficient statistic.
Uniformly minimum variance unbiased estimator. Methods of Estimation: Maximum likelihood method, moments, minimum Chi-square and modified minimum Chi-square methods. Properties of maximum likelihood estimator (without proof). Confidence intervals: Determination of confidence intervals based on large samples, confidence intervals based on small samples.
Statistical Hypothesis: Simple and composite, procedure of testing of hypothesis, critical region, types of errors, level of significance ,power of a test., most powerful test and Neyman-Pearson lemma.
Sequential Analysis: Definition and construction of S.P.R.T. Fundamental relation among, A and B. Wald’s inequality for testing null hypothesis v/s alternative hypothesis. Determination of A and B Average sample number and operating characteristic curve.
Non-Parametric Tests: Sign tests, signed rank test, Kolmogorov-Smirnov one sample test. General two sample problems: Wolfowitz runs test, Kolmogorov Smirnov two sample test (for sample of equal size), Median test, Wilcoxon-Mann-Whitney U test. Test of randomness using run test based on the total number of runs and the length of a run. Kendall’s Tau test for independence of correlation
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
