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Statistical Inference

Statistical Inference. Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur. This course covers some important topics in statistical inference. Point Estimation: unbiasedness, consistency, efficiency, method of moments, maximum likelihood estimations, method of lower bounds, sufficiency and completeness. Testing of Hypotheses: determination of most powerful & uniformly most powerful tests, likelihood ratio tests. Interval Estimation: methods for finding confidence intervals, shortest length confidence intervals. (from nptel.ac.in)

Lecture 25 - Uniformly Most Powerful (UMP) Tests (cont.)

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Lecture 01 - Introduction and Motivation

Lecture 02 - Basic Concepts of Point Estimations I

Lecture 03 - Basic Concepts of Point Estimations II

Lecture 04 - Finding Estimators I

Lecture 05 - Finding Estimators II

Lecture 06 - Finding Estimators III

Lecture 07 - Properties of Maximum Likelihood Estimation

Lecture 08 - Lower Bounds for Variance I

Lecture 09 - Lower Bounds for Variance II

Lecture 10 - Lower Bounds for Variance III

Lecture 11 - Lower Bounds for Variance IV

Lecture 12 - Sufficiency

Lecture 13 - Sufficiency and Information

Lecture 14 - Minimal Sufficiency, Completeness

Lecture 15 - Uniformly Minimum-Variance Unbiased (UMVU) Estimation, Ancillarity

Lecture 16 - Invariance I

Lecture 17 - Invariance II

Lecture 18 - Bayes and Minimax Estimation I

Lecture 19 - Bayes and Minimax Estimation II

Lecture 20 - Bayes and Minimax Estimation III

Lecture 21 - Testing of Hypotheses: Basic Concepts

Lecture 22 - Neyman-Pearson Fundamental Lemma

Lecture 23 - Applications of Neyman-Pearson Lemma

Lecture 24 - Uniformly Most Powerful (UMP) Tests

Lecture 25 - Uniformly Most Powerful (UMP) Tests (cont.)

Lecture 26 - UMP Unbiased Tests

Lecture 27 - UMP Unbiased Tests (cont.)

Lecture 28 - UMP Unbiased Tests: Applications

Lecture 29 - Unbiased Tests for Normal Populations

Lecture 30 - Unbiased Tests for Normal Populations (cont.)

Lecture 31 - Likelihood Ratio Tests I

Lecture 32 - Likelihood Ratio Tests II

Lecture 33 - Likelihood Ratio Tests III

Lecture 34 - Likelihood Ratio Tests IV

Lecture 35 - Invariant Tests

Lecture 36 - Test for Goodness of Fit

Lecture 37 - Sequential Procedure

Lecture 38 - Sequential Procedure (cont.)

Lecture 39 - Confidence Intervals

Lecture 40 - Confidence Intervals (cont.)