Statistical Theory: Inference and Sufficiency

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Statistical Theory: Cramér-Rao Bound & Hypothesis Testing

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

Confidence Intervals: Definition and Estimation

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

Interval Estimation: Method of Moments

Covers the method of moments for estimating parameters and constructing confidence intervals based on empirical moments matching distribution moments.

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.

Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

Eliminating Nuisance Parameters: Statistical Inference

Covers the elimination of nuisance parameters in statistical inference using Lemmas 14 and 15.

Exponential Family: Maximum Entropy Distributions

Covers exponential families and maximum entropy distributions under moment constraints.

Probability Models: Fundamentals

Introduces the basics of probability models, covering random variables, distributions, and statistical estimation.

Likelihood Ratio Tests: Optimality and Applications

Explores the theory and applications of likelihood ratio tests in statistical hypothesis testing.

Statistical Analysis: Data Exploration and Inference

Covers statistical analysis, emphasizing data exploration and inference to quantify uncertainty and draw conclusions.