Maximum Likelihood Estimation: Properties and Applications

This lecture, given by the instructor on October 18, 2021, delves into the concept of Maximum Likelihood Estimation (MLE). The lecture covers topics such as taking partial derivatives to find MLE, verifying the maximum, and examples of MLE for Gaussian and Poisson trials. It also explores the equi-variance of MLEs, consistency of MLE in exponential families, and the distribution of MLE. The lecture concludes with discussions on the properties and assumptions related to MLE, including the consistency of MLE in different scenarios and the implications of regularity conditions. Through various examples and derivations, the lecture provides a comprehensive understanding of MLE and its applications.