# Mathematics - Statistical Inference

Indian Institute of Technology Kharagpur

Course contents:

Point Estimation: Parametric point estimation, unbiasedness, consistency, efficiency, method of moments and maximum likelihood, lower bounds for the variance of an estimator, Frechet-Rao-Cramer, Bhattacharya, Chapman-Robbins-Kiefer inequalities. Sufficiency, minimal sufficiency, Factorization Theorem, Rao-Blackwell Theorem, completeness, Lehmann-Scheffe Theorem, UMVUE, Basu’s Theorem, invariance, best equivariant estimators.

Testing of Hypotheses: Tests of hypotheses, simple and composite hypotheses, types of error, Neyman-Pearson Lemma, families with monotone likelihood ratio, UMP, UMP unbiased and UMP invariant tests. Likelihood ratio tests - applications to one sample and two sample problems, Chi-square tests. Wald’s sequential probability ratio test.

Interval estimation: methods for finding confidence intervals, shortest length confidence intervals.

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