Theory of Statistics III

3 credits · Graduate

The main goal of this course is to expose students to modern ideas in statistical theory to bring them to the frontier of research. We will study: (1) testing problems in high dimensions understanding the performance of Bonferroni's method, Fisher's test, chi-square tests, and the higher criticism under sparse alternatives with strong effects and denser alternatives with mild effects; (2) multiple testing problems, the familywise error rate (FWER) and procedures for controlling the FWER, false discovery rate (FDR), Benjamini-Hochberg procedure; (3) conditional testing and controlled variable selection via knockoffs; (4) combining results from several tests via e-values and anytime valid inference; (5) topics in selective inference such as false coverage rate and post-selection inference; (6) conformal/predictive inference; (7) permutation testing and its modern applications in model-free inference ; (8) James-Stein estimation; (9) empirical Bayes methods.