Stochastic Simulation: Low-Discrepancy Point Sets

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

Estimation Methods: Bias-Variance Tradeoff

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

Statistical Inference: Approximate Critical Values and Confidence Intervals

Covers the construction of confidence intervals and approximate critical values in statistical inference.

Nonparametric and Bayesian Statistics

Covers nonparametric statistics, kernel density estimation, Bayesian principles, and posterior distribution summarization.

Statistical Inference

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

Monte Carlo Method: Simulation and Inference

Covers the Monte Carlo method for statistical inferences using simulation tools and sample mean estimators.

Optimality in Statistical Inference

Delves into the duality between confidence intervals and hypothesis tests, emphasizing the importance of precision and accuracy in estimation.

Interval Estimation

Covers the construction of confidence intervals for a normal distribution with unknown mean and variance.

Statistical Theory: Inference and Optimality

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.

Point Estimation Methods: MOM and MLE

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