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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

Description:

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.

Parameter Estimation

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#Mathematics #Statistics & Probability #Parameter Estimation #Maximum Likelihood Estimation