This course on Parameter Estimation covers various methods for estimating parameters and their optimality properties. The learning outcomes include understanding concepts such as Maximum Likelihood Estimation, Bayes Estimation, Sufficient Statistics, Fisher-Neyman Factorization Theorem, and Basu's Theorem. Students will also learn about unbiased estimation, mean squared error, and the Cramer-Rao Lower Bound. The course teaches skills in empirical substitution, Bayesian estimation, and complete statistics. The teaching method involves video lectures explaining different estimation techniques. This course is intended for individuals interested in statistics, data analysis, and research who want to deepen their understanding of parameter estimation methods.
Overview
Syllabus
Empirical Substitution: Frequency Substitution.
Empirical Substitution: Method of Moments.
Maximum Likelihood Estimation.
Prior and Posterior Distributions.
Bayes Estimation.
Bayes Estimation for the Variance of a Normal Distribution.
Bayesian Estimation - General Linear Model.
Sufficient Statistic.
Fisher-Neyman Factorization Theorem.
One-to-One Functions of Sufficient Statistics.
Sufficient Statistics - Examples.
Jointly Sufficient Statistics - Examples.
Distribution of a sufficient statistics from a 1-parameter exponential family.
Minimal Sufficient Statistics.
Minimally Sufficient Statistic and Maximum Likelihood Estimation.
Ancillary Statistic.
Ancillary Statistic: Example.
Complete Statistics.
Basu's Theorem.
Basu's Theorem: Examples.
Unbiased Estimate and Mean Squared Error.
Unbiased Estimates for Population Std Dev using the Sample Mean Absolute Dev and the Sample Std Dev.
Normal Unbiased Estimator implies the Mean Absolute & square-root Mean Squared Loss are Proportional.
Rao - Blackwell Theorem.
Lehmann - Scheffe Theorem.
Fisher's Information: Examples.
Fisher's Information: Cauchy Distribution.
Cramer-Rao Lower Bound / Inequality.
Exponential Family: Cramer-Rao Lower Bound.
Taught by
statisticsmatt
