The Stein Phenomenon and Superefficiency

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Statistical Theory: Maximum Likelihood Estimation

Explores the consistency and asymptotic properties of the Maximum Likelihood Estimator, including challenges in proving its consistency and constructing MLE-like estimators.

Optimality in Decision Theory: Unbiased Estimation

Explores optimality in decision theory and unbiased estimation, emphasizing sufficiency, completeness, and lower bounds for risk.

Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

Statistical Theory: Cramér-Rao Bound & Hypothesis Testing

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

Basic Principles of Point Estimation

Explores the Method of Moments, Bias-Variance tradeoff, Consistency, Plug-In Principle, and Likelihood Principle in point estimation.

Estimators and Confidence Intervals

Explores bias, variance, unbiased estimators, and confidence intervals in statistical estimation.

Fisher Information, Cramér-Rao Inequality, MLE

Explains Fisher information, Cramér-Rao inequality, and MLE properties, including invariance and asymptotics.

Statistical Models and Parameter Estimation

Explores statistical models, parameter estimation, and sampling distributions in probability and statistics.

Estimators and Bias

Explores estimators, bias, and efficiency in statistics, emphasizing the trade-off between bias and variability.

Confidence Intervals: Definition and Estimation

Explains confidence intervals, parameter estimation methods, and the central limit theorem in statistical inference.