Syllabus
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Course Code: ST-203 Course Name: Inference-I |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Elements of Statistical Inference. Concept of likelihood function. Point estimation. Concept of consistency, unbiased estimators, correction for bias, minimum variance estimator, Cramer – Rao inequality, Minimum Variance-Bound (M.V.B.) estimator, Bhattacharya Bounds, Uniqueness of minimum variance estimators, efficiency, Minimum mean- square estimation. |
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| 2 | Sufficient statistic, Neymann factorization theorm sufficiency and minimum variance. Rao- Blackwell theorem. Lehman Schefe's theorem. Distributions possessing sufficient statistics. Sufficiency when range depends on the parameter. The method of Least squares, The Least Squares estimator in the linear model, Optimum properties, Estimation of variance, the normality assumption. |
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| 3 | Methods of estimation : Method of moments, Method of minimum chi-square and modified minimum chi-square , Method of maximum likelihood estimators and their properties, sufficiency, consistency of ML estimators. Hazurbazar’s theorem, unique consistent ML estimators, efficiency and asymptotic normality of ML estimators. |
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| 4 | Interval estimation : Confidence intervals, confidence statements , central and non-central intervals , confidence intervals, Most selective intervals , Fiducial intervals : Fiducial inference in student’s distribution , Problem of two means and its fiducial solution . Exact confidence intervals based on student’s distribution, Approximate confidence- intervals solutions. Elementary Bayesian inference: Ideas of subjective probability, prior and posterior distribution, Bayesian intervals, Discussion of the methods of interval estimation. |
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