Statistical Theory: Maximum Likelihood Estimation

This lecture delves into the consistency of the Maximum Likelihood Estimator (MLE) and its asymptotic properties. It explores the relationship between the MLE and the Kullback-Leibler Divergence, highlighting the challenges in proving the MLE's consistency. The lecture discusses deterministic examples to illustrate the complexities of the MLE's behavior. It also covers the construction of asymptotically MLE-like estimators and the Newton-Raphson algorithm. The lecture concludes with a discussion on misspecified models and likelihood, emphasizing the importance of model approximation and the behavior of estimators in such scenarios.