STA 355: Theory of statistical practice
Wenlong Mou, Department of Statistical Sciences, University of Toronto, Fall 2026
Schedule
| lecture | topic | book chapters | notes |
| 09/11 | review of probability theory, probability inequalities, convergence of random variables, laws of large numbers, central limit theorem, Slutsky's theorem | 1 – 5 | Lecture 1 |
| 09/18 | arithmetic of probabilistic convergence, small-o and big-O notation in probability, delta method, statistical models, point estimation, confidence sets | 5, 6 | Lecture 2 |
| 09/25 | hypothesis testing basics, empirical CDF and confidence bands, plug-in and quantile estimation, introduction to bootstrap | 7, 8 | Lecture 3 |
| 10/02 | bootstrap resampling and Monte Carlo simulation, bootstrap standard errors, normal, pivotal and percentile confidence intervals, bootstrap failure for the sample maximum, validity for sample averages and Hadamard differentiability | Wasserman, Chapter 8; supplementary: van der Vaart 20.2, 23.2 | Lecture 4 |
| 10/09 | parametric bootstrap, Z- and M-estimation, method of moments and maximum likelihood, consistency of M-estimators, uniform laws of large numbers and Wald's theorem | Wasserman, Chapters 8–9; supplementary: van der Vaart 5.1–5.2, 5.5 | Lecture 5 |
| 10/16 | identifiability and MLE consistency, asymptotic normality of Z- and M-estimators, sandwich covariance and plug-in inference, Fisher information and the Cramer–Rao bound, Newton and one-step estimators, averaged stochastic gradient descent | Wasserman 9.5, 9.7–9.8, 9.10, 9.13.4; supplementary: van der Vaart 5.2–5.3, 5.5–5.7 | Lecture 6 |
| 10/23 | | | |
| 11/06 | | | |
| 11/13 | | | |
| 11/20 | | | |
| 11/27 | | | |
| 12/04 | | | |
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