This is a continuing course to Advanced Theory of Statistics. We will cover an introduction to empirical process theory, semiparametric
statistics, and nonparametric statistics.
| Week | Date | Topics | References | Assignments |
| 1 | 2/21 | No class | | |
| 2 | 2/28 | Introduction, stochastic convergence in metric spaces | vdV Chap. 18, Kosorok Chaps. 6 and 7 | |
| 3 | 3/7 | Classical empirical processes, Glivenko–Cantelli and Donsker results via bracketing | vdV Secs. 19.1 and 19.2, Kosorok Chap. 8 | Homework 1 |
| 4 | 3/14 | Glivenko–Cantelli and Donsker results via uniform covering, preservation results | vdV Sec. 19.2, Kosorok Chaps. 8 and 9 | |
| 5 | 3/21 | Random functions, changing classes, functional delta method | vdV Secs. 19.4 and 19.5, Chap. 20, Kosorok Chap. 12 | |
| 6 | 3/28 | M- and Z-estimators: consistency and asymptotic normality | vdV Secs. 5.1–5.3, Kosorok Chaps. 13 and 14 | Homework 2 |
| 7 | 4/4 | Qingming Festival | | |
| 8 | 4/11 | Examples of M- and Z-estimators, maximum likelihood estimators | vdV Secs. 5.3 and 5.5 | |
| 9 | 4/18 | Semiparametric models, Banach and Hilbert spaces, tangent sets and efficiency | vdV Secs. 25.1–25.3, Kosorok Chaps. 17 and 18 | |
| 10 | 4/25 | Efficient score functions and information, semiparametric inference via efficient score equations | vdV Secs. 25.4 and 25.8, Kosorok Chap. 19 | |
| 11 | 5/2 | Semiparametric inference via general estimating equations and maximum likelihood | vdV Secs. 25.9–25.12, Kosorok Chaps. 20 and 21 | Homework 3 |
| 12 | 5/9 | Nonparametric models, kernel density estimators, cross-validation | Tsybakov Secs. 1.1, 1.2, and 1.4 | |
| 13 | 5/16 | The Nadaraya–Watson estimator, local polynomial estimators, projection estimators | Tsybakov Secs. 1.5–1.7 | |
| 14 | 5/23 | Minimax lower bounds | Tsybakov Chap. 2 | Homework 4 |
| 15 | 5/30 | Duanwu Festival | | |
| 16 | 6/6 | Final presentation | Project topics |
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