Covers Likelihood Ratio Tests, their optimality, and extensions in hypothesis testing, including Wilks' Theorem and the relationship with Confidence Intervals.
Explores the Stein Phenomenon, showcasing the benefits of bias in high-dimensional statistics and the superiority of the James-Stein Estimator over the Maximum Likelihood Estimator.
Explores extreme values in random variables, applications in environmental factors, reliability modeling, block maxima distribution, and the Generalized Extreme Value distribution.
Explores statistical inference, sufficiency, and completeness, emphasizing the importance of sufficient statistics and the role of complete statistics in data reduction.
Covers methods to define the design storm, empirical distribution of rainfall maxima, Gumbel distribution, and intensity-duration-frequency relationships.