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Maj/Stat-401  : Statistical Inference-I

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Course Contents

Concept and problems of estimation. Properties of estimators namely unbiasedness, consistency, sufficiency, efficiency, mean square error consistency and best asymptotic normal estimator. Minimal sufficient statistics joint sufficiency. Exponential family. Sufficiency and completeness. Cramer-Rao inequality and its applications. Minimum variance bound estimators. Rao-Blackwell and Lehman Scheffe theorems and their applications. Uniformly minimum variance unbiased estimators joint completeness.

Course Synopsis

To familiarize students with properties of good point estimators, minimal sufficiency and completeness.

Course Learning Outcomes

• Explain the notion of a parametric model and point estimation of the parameters of those models. Explain and apply approaches to include a measure of accuracy for estimation. • To understand the techniques in the areas of point estimation and the implementation of various statistical inferential approaches.


Introduction to Estimation Theory by Barry Van Veen

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Point Estimators by Brandon Foltz

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Good estimator properties by Ben Lambert

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Unbiased Estimators by IBvodcasting ibvodcasting

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The Sample Variance is an Unbiased Estimator of the Population Variance by jbstatistics

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The Sample Mean is an Unbiased Estimator of the Population Mean by Maths and Stats

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Unbiased Estimators Binomial Example by IBvodcasting ibvodcasting

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PROPERTY OF ESTIMATION (consistency, efficiency& sufficiency) by SOURAV SIR'S CLASSES

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Consistent Estimator of Sample Variance from Normal Population by Mohammad Nasir Abdullah

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Calculating Bias and Efficiency by Wang-Zhao-Liu Q

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Most efficient estimator and efficiency by Cse Girl

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Minimum Variance Bound Estimator by duraid badr

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The minimum variance unbiased estimator (MVUE) by Karl Gregory

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Introduction to Cramer-Rao Lower Bound by Timothy Schulz

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Cramer-Rao lower bound(CRLB), efficient estimators, MVUE, example by Phil Chan

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Examples on Cramer-Rao Bound by Probability, Stochastic Processes - Random Videos

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An introduction to the concept of a sufficient statistic by Ben Lambert

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Sufficient Statistics by Joe Stickles

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Minimal Sufficient Statistics for the Poisson distribution by deetoher

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Minimal Sufficient Statistics for the Binomial distribution by deetoher

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Minimal Sufficient Statistics for the Beta distribution by deetoher

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Gamma Distribution: Member of the Exp Family by deetoher

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Poisson distribution: a member of the exp family by deetoher

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Negative Binomial - a member of the Natural Exponential Family by deetoher

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Neyman Fisher Factorization Theorem by Anish Turlapaty

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Rao-Blackwell Theorem by math et al

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Rao Blackwell Theorem and MVUEs by Michael Satz

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Confidence Interval for a population mean - σ known by Joshua Emmanuel

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Book Title : INTRODUCTION TO THE THEORY OF STATISTICS
Author : Mood, Alexander McFarlane, Graybill. Franklin A., Boes, Duane C.
Edition : Third Edition
Publisher : McGraw-Hill, Inc.
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Book Title : Introduction to Mathematical Statistics
Author : Robert V. Hogg, Joseph W. McKean, Allen T. Craig
Edition : Seventh Edition
Publisher : Pearson Education, Inc.
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Title : unbiasedness, consistency, efficiency
Type : Presentation

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Title : Sufficiency and Rao Blackwell theorem
Type : Presentation

View Sufficiency and Rao Blackwell theorem

Title : Cramer Rao Lower Bound
Type : Presentation

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Title : Properties of estimator
Type : Presentation

View Properties of estimator