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 |