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Last updated:

September 23, 2023

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FREE

This course includes:

Unlimited Duration

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Description

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)

Course Curriculum

  • Lecture 01 – Introduction and Motivation Unlimited
  • Lecture 02 – Basic Concepts of Point Estimations I Unlimited
  • Lecture 03 – Basic Concepts of Point Estimations II Unlimited
  • Lecture 04 – Finding Estimators I Unlimited
  • Lecture 05 – Finding Estimators II Unlimited
  • Lecture 06 – Finding Estimators III Unlimited
  • Lecture 07 – Properties of Maximum Likelihood Estimation Unlimited
  • Lecture 08 – Lower Bounds for Variance I Unlimited
  • Lecture 09 – Lower Bounds for Variance II Unlimited
  • Lecture 10 – Lower Bounds for Variance III Unlimited
  • Lecture 11 – Lower Bounds for Variance IV Unlimited
  • Lecture 12 – Sufficiency Unlimited
  • Lecture 13 – Sufficiency and Information Unlimited
  • Lecture 14 – Minimal Sufficiency, Completeness Unlimited
  • Lecture 15 – Uniformly Minimum-Variance Unbiased (UMVU) Estimation, Ancillarity Unlimited
  • Lecture 16 – Invariance I Unlimited
  • Lecture 17 – Invariance II Unlimited
  • Lecture 18 – Bayes and Minimax Estimation I Unlimited
  • Lecture 19 – Bayes and Minimax Estimation II Unlimited
  • Lecture 20 – Bayes and Minimax Estimation III Unlimited
  • Lecture 21 – Testing of Hypotheses: Basic Concepts Unlimited
  • Lecture 22 – Neyman-Pearson Fundamental Lemma Unlimited
  • Lecture 23 – Applications of Neyman-Pearson Lemma Unlimited
  • Lecture 24 – Uniformly Most Powerful (UMP) Tests Unlimited
  • Lecture 25 – Uniformly Most Powerful (UMP) Tests (cont.) Unlimited
  • Lecture 26 – UMP Unbiased Tests Unlimited
  • Lecture 27 – UMP Unbiased Tests (cont.) Unlimited
  • Lecture 28 – UMP Unbiased Tests: Applications Unlimited
  • Lecture 29 – Unbiased Tests for Normal Populations Unlimited
  • Lecture 30 – Unbiased Tests for Normal Populations (cont.) Unlimited
  • Lecture 31 – Likelihood Ratio Tests I Unlimited
  • Lecture 32 – Likelihood Ratio Tests II Unlimited
  • Lecture 33 – Likelihood Ratio Tests III Unlimited
  • Lecture 34 – Likelihood Ratio Tests IV Unlimited
  • Lecture 35 – Invariant Tests Unlimited
  • Lecture 36 – Test for Goodness of Fit Unlimited
  • Lecture 37 – Sequential Procedure Unlimited
  • Lecture 38 – Sequential Procedure (cont.) Unlimited
  • Lecture 39 – Confidence Intervals Unlimited
  • Lecture 40 – Confidence Intervals (cont.) Unlimited

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