Likelihood Ratio Test: Hypothesis Testing

This lecture covers the concept of hypothesis testing, focusing on the likelihood ratio test. It explains the Neyman-Pearson lemma, the most powerful test, and the conditions for its optimality. The lecture delves into examples, such as the Poisson distribution and the Bernoulli distribution, to illustrate the application of hypothesis testing. It also discusses the challenges of finding uniformly most powerful tests and the non-existence of such tests in certain scenarios. The lecture concludes with the asymptotic approximations and Wilks' Theorem, providing insights into the statistical properties of hypothesis testing.