Fisher Information, Cramér-Rao Inequality, MLE

This lecture covers the definition of the score function, Fisher information, and Cramér-Rao inequality. It explains how the Fisher information measures the amount of information in a sample and how the Cramér-Rao inequality provides a lower bound on the variance of unbiased estimators. The invariance of the maximum likelihood estimator (MLE) under bijections is also discussed, along with the asymptotics of the MLE obtained from i.i.d. observations.