Coming soon
Statistical Inference-II
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.
Students will able to
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Course |
Learning outcomes (at course level |
Learning and teaching strategies |
Assessment Strategies
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Paper Code |
Paper Title |
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STT-321 |
Statistical Inference-I |
CO 51: Know the notion of a parametric model and point estimation of the parameters of those models.
CO 52: Developing/ constructing best/most powerful statistical tests to test hypotheses regarding unknown population parameters Using Neyman-Pearson Lemma and Likelihood Ratio tests.
CO 53: Explain in detail elements of statistical decision problems and various inference problems viewed as decision problem.
CO 54: Explain in detail approaches to include a measure of accuracy for estimation procedures and our confidence in them by examining the area of interval estimation.
CO 55: Used Basic principle of Bayesian estimation for finding posterior distributions of unknown Population parameters.
CO 56: Choose appropriate methods of inference to tackle real problems. |
Approach in teaching: Interactive Lectures, Group Discussion, Classroom Assignment Problem Solving Sessions
Learning activities for the students: Assignments Seminar Presentation Subject based Activities |
Classroom Quiz Assignments Class Test Individual Presentation |
Location Invariance, scale invariance. Pitmann’s estimators for location and scale parameters. Pitman concept of closeness of estimator. Proof of the properties of M.L.E(large samples), Huzur Bazaar theorem
Consistent asymptotic normal (CAN) estimator, invariance property of likelihood estimator. Wilks likelihood ratio criteria and the various test based on it.
Asymptotic distribution of likelihood ratio statistic. Bartlett's test for homogeneity of variances. Randomized tests. Generalized Neyman- Pearson lemma.
Uniformly most powerful tests for two-sided hypothesis. Unbiased tests. Uniformly most powerful unbiased tests, Generalized 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. ε-bayes & minimax decision rule, Generalized Bayes rule.
- Casela G & Berger RL. (2002): Statistical Inference. Duxbury Thompson Learning.
- Conover WJ. (1980): Practical Nonparametric Statistics. John Wiley.
- Kiefer JC. (1987): Introduction to Statistical Inference. Springer.
- Lehmann EL. (1986) Theory of Point Estimation. John Wiley.
- Wald A. (2004) Sequential Analysis. Dover Publ.
- Cramer, H.(1946) : Mathematical methods of Statistics, Princeton University Press.
- Goon and others.(2003): Outline of Statistical theory Vol-I, World Press.
- Rao,C.R. (1973) : Linear Statistical inference and its applications, 2nd Ed,
- John Wiley & Sons Inc.
- Gibbons,J.D. (2010): Non- Parametric Statistical Inference, McGraw-Hill, fifth edition.
- Kendall, M.G. and Stuart, A. (1971): Advanced Theory of Statistic Vol. I and II,Charles Griffin.
- Mood, Graybill and Boes. (1974): Introduction to the theory of Statistics 3rded, McGraw- Hill.
- Hogg,R.V. and Craig,A.T.( (1971): Introduction to Mathematical Statistics, Princeton University Press.
- Rao, C. R. (2002): Linear Statistical Inference and its Applications, Willey- Blackwell
- Gibbons (1971): Non Parametric Inference, Chapman and Hall
- Sidney and Siegal (1956): Non Parametric for Behavioral science, Mcgraw-Hill Book Company
