STA3000F
Home
Schedule

STA3000F: Advanced Theory of Statistics

Wenlong Mou, Department of Statistical Sciences, University of Toronto, Fall 2024

Schedule

lecture topic references notes
09/06 Probability recap, decision theory, admissibility, Bayes and minimax procedures Larry Wasserman's notes, Bickel and Doksum 1.3; Keener 7.1, 7.2; Jon Wellner's notes (Section 1-6) Lecture 1
09/13 Decision theory continued, sufficiency and completeness, unbiased estimation Bickel and Doksum 3.3, Keener 3.3, 3.5, 3.6, 4.1, Jon Wellner's notes Lecture 2
09/20 UMVU estimation continued, log-likelihood and Fisher information, Cramér–Rao lower bound and Van Trees inequality Jon Wellner's notes, Keener 4.5, 4.6, Tsybakov 2.7.3 Lecture 3
09/27 Framework for testing, Neyman–Pearson lemma, UMP tests, Two-sided tests and UMPU, distance between probability measures, minimax testing Keener Chapter 12 (except for 12.5), Tsybakov 2.4, Siva's notes Lecture 4
10/04 minimax testing lower bounds, basics of probablistic convergence, uniform law of large numbers and covering/packing Siva's notes, van der Vaart 2.1, 2.2, 3.1, 3.3, 5.2, Peter's notes Lecture 5
10/11 Wald's consistency theorem, symmetrization and chaining, main empirical process bound van der Vaart 5.2, van der Vaart and Wellner 2.3, 2.5, Bohdi's notes, Section 5 Lecture 6
10/18 VC (subgraph) dimension with application to empirical process theory, Sauer's lemma, fat-shattering dimension, main convergence rate theorem van der Vaart and Wellner 2.6.1, 2.6.2, 3.2.2, Aditya's notes, Section 10, 11Lecture 7
10/25 Examples of convergence rates, asymptotic distribution, stochastic equicontinuity and process convergence van der Vaart Chapter 19, Aditya's notes, Section 21, 22, 23Lecture 8
11/08 Bayesian posterior convergence, Schwartz's theorem, least-square estimator for nonparametric regression, covering number for Hölder classes Chapter 7 of the monograph, van der Vaart and Wellner 2.7.1, Martin J. Wainwright high-dimensional statistics Chapter 13Lecture 9
11/15 Convergence rates of least square estimators continued, projection estimator, kernel density estimation for Hölder and Sobolev classes, lack of asymptotic optimality Tsybakov 1.2, 1.7, c.f. the paper for sub-optimality of constrained least squares Lecture 10