STA3000F: Advanced Theory of Statistics

Wenlong Mou, Department of Statistical Sciences, University of Toronto, Fall 2025

Schedule

lecture	topic	references	notes
09/05	Probability recap, basic concentration inequalities, decision theory, admissibility	Larry Wasserman's notes on concentration, Gilbert–Varshamov bound for Hamming packing, Bickel and Doksum 1.3	Lecture 1
09/12	Bayes and minimax decision rules, application of duality to decision theory, sufficient statistics	Murat's notes, Chapter 1 on Stein's phenomenon, Bickel and Doksum 3.2, 3.3, Keener 3.2, Jon Wellner's notes	Lecture 2
09/19	UMVU estimation, Fisher information, (Bayesian) Cramér-Rao lower bound	Jon Wellner's notes, Keener 4.5, 4.6, Tsybakov 2.7.3	Lecture 3
09/26	Bayesian Cramér-Rao continued, local minimax lower bound, testing framework, Neyman-Pearson lemma and UMP tests, Le Cam's two-point method	Keener Chapter 12 (except for 12.5), Tsybakov 2.3, 2.4, 2.7.3	Lecture 4
10/03	two-sided testing, minimax testing radius, basics of uniform convergence, covering and packing numbers	Keener Chapter 12, Siva's notes on minimax testing upper bounds and lower bounds, Peter's notes	Lecture 5
10/10	Wald's consistency theorem, symmetrization and Rademacher complexity, Dudley chaining integral, main empirical process bounds	van der Vaart 5.2, van der Vaart and Wellner 2.3, 2.5, Bohdi's notes, Section 4	Lecture 6
10/17	main empirical process bound, VC dimension, Sauer's lemma, bounds on covering/packing number using VC dimension	van der Vaart and Wellner 2.6.1, 2.6.2, Bohdi's notes, Section 7	Lecture 7
10/24	VC subgraph dimension, fat shattering dimension, localization and convergence rates	Aditya's notes Lecture 11 – 13, van der Vaart and Wellner 3.2.2	Lecture 8
11/07
11/14
11/21
11/28