Lectures related to Stochastic Simulation: Low-Discrepancy Point Sets

Estimators and Confidence Intervals

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

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Confidence Intervals: Gaussian Estimation

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

Confidence Intervals: Definition and Estimation

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

Monte Carlo Estimation: Error Analysis

Covers the Monte Carlo method for generating realizations and unbiased estimators.

Probability and Statistics II: Estimation and Hypothesis Testing

Covers the Central Limit Theorem, confidence intervals, hypothesis testing, and qualities of estimators.

Estimating Parameters: Confidence Intervals

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

Confidence Intervals: Student, Asymptotic Wald

Covers confidence intervals for Gaussian means, Student distribution, and Wald confidence intervals for maximum likelihood estimators.

Estimation Criteria

Covers criteria for estimating parameters, emphasizing the importance of consistency, bias, variance, and efficiency of estimators.

Estimation Methods in Probability and Statistics

Discusses estimation methods in probability and statistics, focusing on maximum likelihood estimation and confidence intervals.

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.

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.