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
11/22 Lack of asymptotic optimality continued, local polynomial estimator, minimax lower bound for estimating the functional at one point Tsybakov 1.5, 1.6, 2.5, Appendix A.1 Lecture 11
11/29 Basics of information theory, Fano's lemma, minimax lower bound for integrated risk, minimax adaptivity and Lepski's method for bandwidth selection Tsybakov 2.6, 2.7.1, Yihong's notes, Chapter 13, 14, Cheng's notes on Lepski's method Lecture 12