Probability and Statistics II: Estimation and Hypothesis Testing

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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.

Statistics: Hypothesis Testing & Confidence Intervals

Covers hypothesis testing, confidence intervals, data distributions, and statistical significance in data analysis.

Estimating Parameters: Confidence Intervals

Explores estimating parameters through confidence intervals in linear regression and statistics.

Estimation Methods: Bias-Variance Tradeoff

Explores the MSE quality measure for estimators and the bias-variance tradeoff.

Statistical Inference

Covers likelihood ratio statistic, confidence intervals, and hypothesis testing concepts.

Point Estimation Methods: MOM and MLE

Explores point estimation methods like MOM and MLE, discussing bias, variance, and examples.

Distribution Theory of Least Squares

Explores the distribution theory of least squares estimators in a Gaussian linear model, focusing on precision and confidence intervals construction.

Linear Regression: Estimation and Inference

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

Likelihood Ratio Tests: Optimality and Extensions

Covers Likelihood Ratio Tests, their optimality, and extensions in hypothesis testing, including Wilks' Theorem and the relationship with Confidence Intervals.