| Lecture Notes | Topics |
|---|---|
| Lecture 1 | review of probability theory |
| Lecture 2 | review of probability theory |
| Lecture 3 | CLT, first-order delta method |
| Lecture 4 | variance stabilizing transformation, second-order delta method |
| Lecture 5 | moment estimators, Taylor expansions |
| Lecture 6 | maximum likelihood estimation |
| Lecture 7 | asymptotic normality, efficiency |
| Lecture 8 | exponential family, ARE, super efficiency |
| Lecture 9 | testing & confidence sets |
| Lecture 10 | testing a subvector, definition of U-statistics |
| Lecture 11 | examples of U-statistics, variance of U-statistics |
| Lecture 12 | Hajek projection |
| Lecture 13 | Hajek projection |
| Lecture 14 | metric entropy, bracketing, uniform laws of large numbers |
| Lecture 15 | Sub-Gaussianity, Hoeffding's inequality |
| Lecture 16 | Symmetrization |
| Lecture 17 | McDiarmid's inequality |
| Lecture 18 | Sub-Gaussian process, Dudley's integral entropy |
| Lecture 19 | Lipschitz functions, VC dimension |
| Lecture 20 | VC dimension |
| Lecture 21 | Convergence rate, Some concepts of convergence in distribution |
| Lecture 22 | Asymptotically equicontinuous |
| Lecture 23 | Donsker Class, Goodness of fit statistics |
| Lecture 24 | Functional delta method |
| Lecture 25 | Bootstrap, Gaussian sequence model |
| Lecture 26 | Soft/hard-thresholding estimators, risk inflation |
| Lecture 27 | Lasso consistency |
Course notes have been folded into the draft Multiplicity, Selection, and Modern Statistical Inference.