Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Introduction to Statistical Inference Level: Undergraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: For Prob III: All limit theorems used in this course will be stated in context with applications. These can be proved in Probability III rigorously. i) Sufficiency, Exponential family, Bayesian methods, Moment methods, Maximum likelihood estimation. ii) Criteria for estimators; UMVUE, Fisher Information. iii) Multivariate normal distribution: Marginals, Conditionals; Distribution of linear forms. iv) Order statistics and their distributions. v) Large sample theory: Consistency, asymptotic normality, asymptotic relative efficiency. vi) Elements of hypothesis testing; Neyman-Pearson Theory, UMP tests, Likelihood ratio and related tests, Large sample tests. vii) Confidence intervals. Reference Texts: (a) George Casella and Roger L Berger: Statistical Inference. (b) Peter J Bickel and Kjell A Doksum: Mathematical Statistics. (c) Erich L Lehmann and George Casella: Theory of Point Estimation. (d) Erich L Lehmann and Joseph P Romano: Testing Statistical Hypotheses. Evaluation:
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Midterm
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[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute] |