Optimality in Statistical Inference

This lecture explores the concept of optimality in statistical inference, focusing on the duality between confidence intervals and hypothesis tests. It discusses the relationship between optimal confidence intervals and optimal hypothesis tests, emphasizing the importance of precision and accuracy in estimation. The lecture also covers the construction of unilateral confidence intervals from unilateral tests, highlighting the conditions under which this approach is valid. Additionally, it delves into the notion of optimal confidence intervals in the context of exponential families, showcasing the interplay between tests and intervals. The instructor, Victor M. Panaretos from EPFL, provides insights into the theoretical foundations of statistical inference, shedding light on the fundamental principles governing optimal estimation.