Lectures related to Semiparametric Inference for Missing-Not-at-Random Data

Confidence Intervals: Definition and Estimation

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

Introduces probability, statistics, distributions, inference, likelihood, and combinatorics for studying random events and network modeling.

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.

The Stein Phenomenon and Superefficiency

Explores the Stein Phenomenon, showcasing the benefits of bias in high-dimensional statistics and the superiority of the James-Stein Estimator over the Maximum Likelihood Estimator.

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.

Statistical Theory: Cramér-Rao Bound & Hypothesis Testing

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

Estimators and Confidence Intervals

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

Model Selection Criteria: AIC, BIC, Cp

Explores model selection criteria like AIC, BIC, and Cp in statistics for data science.

Statistical Theory: Fundamentals

Covers the basics of statistical theory, including probability models, random variables, and sampling distributions.

Linear Regression: Model Adjustment and Parameter Estimation

Explains the decomposition of total sum of squares, model adjustment, and parameter estimation in linear regression.

Red bus/Blue bus paradox

Explores the Red bus/Blue bus paradox, nested logit models, and multivariate extreme value models in transportation.

Density of States and Bayesian Inference in Computational Mathematics

Explores computing density of states and Bayesian inference using importance sampling, showcasing lower variance and parallelizability of the proposed method.

Implicit Generative Models

Explores implicit generative models, covering topics like method of moments, kernel choice, and robustness of estimators.

Estimators and Bias

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

Statistical Models and Parameter Estimation

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

Basic Principles of Point Estimation

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

Parametric Models: Regression Estimators and Optimization

Covers parametric models, regression estimators, and optimization in statistical modeling.

Statistical Estimation: Gaussian Linear Model

Delves into statistical estimation, highlighting the Gaussian linear model and the limitations of ML estimators.

Linear Regression: Statistical Inference and Regularization

Covers the probabilistic model for linear regression and the importance of regularization techniques.