Statistical Theory: Inference and Optimality

This lecture covers topics such as constructing confidence regions from confidence intervals, inverting hypothesis tests, and the pivotal method. It also discusses the relationship between confidence intervals and hypothesis tests, the Bonferroni method, multiple testing, and confidence intervals based on maximum likelihood estimation asymptotics. The instructor emphasizes the importance of likelihood methods in statistical inference, asymptotic results, and the efficiency of statistical approaches. The lecture concludes with insights on misspecification, computational aspects, and the limitations of optimality in statistical methods.