Hypothesis Testing: Wilks' Theorem

This lecture covers hypothesis testing using Wilks' Theorem, focusing on likelihood ratio statistics and asymptotic approximations. It discusses the testing setup, the consistency of maximum likelihood estimators, and the importance of p-values in determining evidence against null hypotheses. The lecture also explores different tests such as Wald's test and the Score test, providing insights into their applications and interpretations. Additionally, it delves into interval estimation, confidence intervals, pivotal quantities, and confidence regions for higher dimensional parameters, emphasizing the significance of these concepts in statistical inference.