Explores the consistency and asymptotic properties of the Maximum Likelihood Estimator, including challenges in proving its consistency and constructing MLE-like estimators.
Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.
Explores maximum likelihood estimation in linear models, covering Gaussian noise, covariance estimation, and support vector machines for classification problems.
Introduces the Generalized Method of Moments (GMM) in econometrics, focusing on its application in instrumental variable estimation and asset pricing models.
Covers methods to define the design storm, empirical distribution of rainfall maxima, Gumbel distribution, and intensity-duration-frequency relationships.
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.