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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)

Introduction


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.)

References
Statistical Inference
Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur. This course covers some important topics in statistical inference.