STA3000F: Advanced Theory of Statistics

Wenlong Mou, Department of Statistical Sciences, University of Toronto, Fall 2026

Schedule

lecture	topic	references	notes
09/11	Radon–Nikodym derivatives, concentration inequalities and the probabilistic method, decision theory, admissibility and James–Stein estimation, Bayes rules	Larry Wasserman's notes on concentration, Gilbert–Varshamov bound for Hamming packing, Bickel and Doksum 1.3	Lecture 1
09/18	Bayes and minimax decision rules, duality and admissibility, sufficient statistics, Rao–Blackwellization, factorization theorem, exponential families, introduction to UMVUE	Murat's notes, Chapter 1, Bickel and Doksum 3.2, 3.3, Keener 3.2, Jon Wellner's notes	Lecture 2
09/25	complete sufficient statistics and UMVUE, Fisher information, classical and Bayesian Cramér–Rao bounds, local minimax risk	Jon Wellner's notes, Keener 3.2, 4.5, 4.6, Tsybakov 2.7.3	Lecture 3
10/02	local minimax and local asymptotic minimax lower bounds, Neyman–Pearson lemma and likelihood ratio tests, total variation and Pinsker's inequality, Le Cam's two-point method, monotone likelihood ratios and UMP tests	Tsybakov 2.3, 2.4, 2.7.3, Keener 12.1–12.3, van der Vaart 8.7	Lecture 4
10/09	two-sided testing and UMPU tests, multivariate Gaussian testing and minimax separation, mixture-prior and chi-squared lower bounds, M-estimation and empirical risk minimization, uniform convergence, covering and packing numbers	Keener 12.5–12.7, Tsybakov 2.4, 2.7.4, van der Vaart 5.1–5.2, 19.2	Lecture 5
10/16	covering–packing duality and volume bounds, Wald's uniform law of large numbers and M-estimator consistency, symmetrization and Rademacher complexity, multiscale chaining and Dudley's entropy integral, uniform entropy bounds for function classes	van der Vaart 5.2, 19.2, 19.6; Vershynin (1st ed.), 4.2, 8.1	Lecture 6
10/23
11/06
11/13
11/20
11/27
12/04