Sampling Distributions: Estimators and Variance

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Covers the concepts of parameter estimation, including unbiased estimators and Fisher information.

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Explores confidence intervals, Gaussian estimation, Cramér-Rao inequality, and Maximum Likelihood Estimators.

Statistical Theory: Cramér-Rao Bound & Hypothesis Testing

Explores the Cramér-Rao bound, hypothesis testing, and optimality in statistical theory.

Estimators: Consistency and Efficiency

Explores the criteria for good estimators, emphasizing consistency and efficiency in estimation.

Maximum Likelihood Estimation

Introduces maximum likelihood estimation for statistical parameter estimation, covering bias, variance, and mean squared error.

Statistical Estimators

Explains statistical estimators for random variables and Gaussian distributions, focusing on error functions for integration.

The Stein Phenomenon and Superefficiency

Explores the Stein Phenomenon, showcasing the benefits of bias in high-dimensional statistics and the superiority of the James-Stein Estimator over the Maximum Likelihood Estimator.

Model Selection Criteria: AIC, BIC, Cp

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Estimation: Linear Estimator

Explores linear estimation, optimal criteria, and the orthogonality principle for good choices in estimation.

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Explores point estimation in statistics, discussing bias, variance, mean squared error, and consistency of estimators.