This course on statistical inference aims to teach students the concepts and techniques related to confidence intervals, likelihood ratio tests, unbiased tests for normal populations, UMP unbiased tests, NP Lemma applications, hypothesis testing, Bayes and Minimax estimation, invariance, UMVU estimation, sufficiency, completeness, lower bounds of variance, properties of MLEs, and finding estimators. The course utilizes a theoretical teaching method and is designed for individuals interested in gaining a deep understanding of statistical inference and its applications.
Overview
Syllabus
Confidence Intervals (Continued).
Confidence Intervals.
Likelihood Ratio Tests - I.
Unbiased Tests for Normal Populations (Continued…).
Unbiased Tests for Normal Populations.
UMP Unbiased Tests : Applications.
UMP Unbiased Tests.
UMP Unbiased Tests.
UMP Tests (Contd.).
UMP Tests.
Applications of NP Lemma.
Neyman Pearson fundamental Lemma.
Testing of Hypothesis : Basic concepts.
Bayes and Minimax Estimation - III.
Invariance - II.
Invariance-I.
UMVU Estimation,Ancillarity.
Minimal Sufficiency,Completeness.
Sufficiency & Information.
Sufficiency.
Lower bounds of variance - IV.
Lower bounds for variance - III.
Lower bounds for variance - II.
Lower bounds for Variance - I.
Properties of MLEs.
Finding Estimators - III.
Finding Estimators - II.
Finding Estimators - I.
Introduction and Motivation.
Basic concepts of point Estimations - I.
Basic concepts of point Estimations - II.
Taught by
Ch 30 NIOS: Gyanamrit
