Concept and problems of estimation. Properties of estimators namely unbiasedness, consistency, sufficiency, efficiency, mean square error consistency and best asymptotic normal estimator. Minimal sufficient statistics joint sufficiency. Exponential family. Sufficiency and completeness. Cramer-Rao inequality and its applications. Minimum variance bound estimators. Rao-Blackwell and Lehman Scheffe theorems and their applications. Uniformly minimum variance unbiased estimators joint completeness.

To familiarize students with properties of good point estimators, minimal sufficiency and completeness.

• Explain the notion of a parametric model and point estimation of the parameters of those models. Explain and apply approaches to include a measure of accuracy for estimation. • To understand the techniques in the areas of point estimation and the implementation of various statistical inferential approaches.

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Book Title : INTRODUCTION TO THE THEORY OF STATISTICS

Author : Mood, Alexander McFarlane, Graybill. Franklin A., Boes, Duane C.

Edition : Third Edition

Publisher : McGraw-Hill, Inc.

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Book Title : Introduction to Mathematical Statistics

Author : Robert V. Hogg, Joseph W. McKean, Allen T. Craig

Edition : Seventh Edition

Publisher : Pearson Education, Inc.

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Title : unbiasedness, consistency, efficiency

Type : Presentation

View unbiasedness, consistency, efficiency

Title : Sufficiency and Rao Blackwell theorem

Type : Presentation

View Sufficiency and Rao Blackwell theorem

Title : Cramer Rao Lower Bound

Type : Presentation

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Title : Properties of estimator

Type : Presentation

View Properties of estimator