Likelihood Ratio Tests: Optimality and Applications

This lecture delves into the theory and applications of likelihood ratio tests, exploring their optimality properties and practical use in statistical hypothesis testing. The Neyman-Pearson paradigm is combined with maximum likelihood estimation to construct powerful tests. The concept of the likelihood ratio statistic is introduced, along with its role in comparing hypotheses. Examples illustrate the application of likelihood ratio tests in various scenarios, including testing for equality of means and exponential distributions. The lecture also covers the asymptotic distribution of the likelihood ratio statistic, as demonstrated by Wilks' Theorem.