Maximum Likelihood Estimation

This lecture covers the concept of Maximum Likelihood Estimation (MLE) in statistical inference, focusing on the estimation of parameters in regular parametric models. It explains the Cramér-Rao bound, the method of maximum likelihood, and the properties of MLE in both discrete and continuous cases. The lecture also discusses the Fisher information and the uniqueness of MLE in exponential families. The instructor provides examples of MLE for Bernoulli, exponential, and Gaussian distributions, highlighting the importance of equivariance in MLE. The lecture concludes with a general proposition on the uniqueness of MLE in one-parameter exponential families.