Explore a comprehensive playlist on parameter estimation techniques, covering empirical substitution, maximum likelihood estimation, Bayesian methods, sufficient statistics, and optimality properties. Learn about Fisher-Neyman factorization, ancillary statistics, complete statistics, unbiased estimates, and the Cramer-Rao lower bound. Dive into specific examples and theorems, including Basu's theorem, Rao-Blackwell theorem, and Lehmann-Scheffe theorem, to gain a thorough understanding of point estimation in statistics.
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
