STA 3000 Winter 2025:

Advanced Theory of Statistics

This course complements the material presented in the Fall semester.

More details can be found in syllabus.

Prof	Piotr Zwiernik
Email	piotr.zwiernik@utoronto.ca
Office hours	Thursday 12pm (UY 9133)

3 homeworks (40%) and in-person final exam (60%), accounting for 50% of the full-year STA3000 course.

The lecture notes (LN) will be updated every week so better not to print the entire document.

Week	Lectures	Suggested reading	HW
1	Exponential families: basic definitions, examples, convexity.	LN 1.1-1.3
2	Exponential families: mean and mixed parametrizations, marginal and conditional distributions.	LN 1.4-1.5
3	Exponential families: KL divergence, Max Entropy Principle, generalized linear models.	LN 1.6-1.7	hw1 out
4	Exponential families: generalized linear models, conjugate priors. Admissibility: admissibility, Rao-Blackwell, SURE, Stein’s paradox.	LN 1.7-1.8 LN 2.4-2.5 check this
5	Multiple testing: motivation, basic definitions, FWER, Bonferroni, Holm	LN 3.2-3.3	hw1 due
6	Multiple testing: FWER vs FDR, Benjamini-Hochberg, Benjamini-Yuketieli Sequential testing: martingales, Wald test, expected stopping time	LN 3.4-3.6	hw2 out
	Reading week. No class.
7	Sequential testing: martingales, Wald test	LN 3.5
8	Sequential testing: expected stopping time in Wald test Universal Inference, E-values	LN 3.6-3.8	hw2 due
9	Concentration of measure: sub-gaussian and sub-exponential variables.	LN 5.1-5.2
10	Concentration of measure: bounded differences ineq., dimension-free concentration ineq.	LN 5.3-5.4	hw3 out
11	Concentration of measure: Maximal inequalities. Applications: sub-Gaussian sequence model	LN 6.1, 7.1
12	Applications: Fixed design linear regression, constrained LS, Stochastic Block Model.	LN 7.2-7.3, 7.5 recording	hw3 due