| lecture | topic | references |
| 09/12 | Probability recap, decision theory, Bayes and minimax procedures | Bickel and Doksum 1.3; Keener 7.1, 7.2; Jon Wellner's notes (Section 1-6) |
| 09/14 | Game theory and minimax procedures, sufficient statistics | Bickel and Doksum 3.3; Keener 3.2, 3.3 |
| 09/19 | Sufficiency, completeness, and UMVU, examples from exponential family | Keener 3.3, 3.5, 3.6, 4.1, Jon Wellner's notes |
| 09/21 | UMVU examples continued; log likelihood, Fisher identity, and Cramér–Rao lower bound | Keener 4.5, 4.6 |
| 09/26 | Hammersley–Chapman–Robbins and Bayesian Cramér–Rao lower bound; framework for testing, Neyman–Pearson lemma, UMP tests | Tsybakov 2.7.3, Keener 12.1, 12.2, 12.3 |
| 09 /28 | Two-sided tests and UMPU, duality between testing and interval estimation; multivariate Gaussian and minimax testing | Keener 12.4, 12.6, 12.7, Siva's notes |
| 10/03 | Minimax testing radius for multivariate Gaussian; Bonus question I; Le Cam's two point method | Siva's notes, Sasha's notes |
| 10/05 | Basics of probabilistic convergence | van der Vaart 2.1, 2.2 |
| 10/10 | Delta methods continued, uniform law of large numbers, covering and packing, Wald's consistency proof for M-estimators and MLE | van der Vaart 3.1, 3.3, 5.2, Keener 9.1, 9.2 |
| 10/12 | Consistency continued; asymptotic distribution of Z-estimators under classical conditions | van der Vaart 5.6, 5.7 |
| 10/17 | Basics of empirical process theory, symmetrization and chaining | John's notes, my notes |
| 10/19 | Examples of empirical process upper bounds, preliminaries of convergence rates | notes, Bohdi's notes, Section 5 |
| 10/24 | Convergence rates of M-estimators, process convergence and Donsker's theorem | notes, van der Vaart 5.3, 5.8 |
| 10/26 | Asymptotic distribution of M estimators via weak convergence of empirical processes, application to MLE | notes, van der Vaart 5.3, 19.4, 19.5 |
| 10/31 | Examples of M-estimator asymptotics. Schwartz's theorem for posterior consistency via testing | notes, van der Vaart 19.5, 7.1 – 7.4 (optional), Chapter 7 of the monograph |
| 11/02 | Bernstein-von-Mises theorem, nonparametric estimation problems, Hölder and Sobolev classes | notes |
| 11/14 | Analysis of least-squares estimators for nonparametric regression, metric entropy for Hölder classes | notes, van der Vaart and Wellner 2.7.1 |
| 11/16 | Kernel density estimation and pointwise risk analysis for Hölder classes | notes, Tsybakov 1.2 |
| 11/21 | MISE for KDE for Sobolev classes, lack of asymptotic optimality, projection estimator | notes, Tsybakov 1.2, 1.7 |
| 11/23 | Projection estimator continued, local polynomial fitting for nonparametric regression | notes, Tsybakov 1.5, 1.6, 1.7 |
| 11/28 | Local polynomial estimation continued; Le Cam's two-point lower bound for pointwise risks; Mutual information and Fano's inequality | notes, Tsybakov 1.6, 2.4, 2.5 |
| 11/30 | Proof of Fano's inequality, lower bounds for integrated risks | notes, Tsybakov 2.6.1, 2.7.1 |
| 12/05 | Adaptive estimation via Lepski's method | |
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