Stats 300B: Theory of Statistics II
Course Schedule
| Lecture Notes | Topics | Reading |
| Tue, Jan 10 | Lecture 1 (tex) | Overview, Convergence of random variables | VDV Chapters 2.1, 2.2 |
| Thu, Jan 12 | Lecture 2 (tex) | Convergence of random variables, delta method | VDV Chapters 2, 3 |
| Tue, Jan 17 | Lecture 3 (tex) | Asymptotic normality, Fisher information | VDV Chapters 3, 4; TPE Chapter 2.5 |
| Thu, Jan 19 | Lecture 4 (tex) | Asymptotic normality, Fisher information | VDV Chapter 3 |
| Tue, Jan 24 | Lecture 5 (tex) | Method of Moments | VDV Chapter 4 |
| Thu, Jan 26 | Lecture 6 (tex) | Superefficiency, U-statistics | VDV Chapter 12 |
| Tue, Jan 31 | Lecture 7 (tex) | U-statistics | VDV Chapter 12 |
| Thu, February 2 | Lecture 8 (tex) | U-statistics, Testing and Confidence Regions | |
| Tue, Feb 7 | Lecture 9 (tex) | Testing, ULLN | Elements of Large Sample Theory 7.7 |
| Thu, Feb 9 | Lecture 10 (tex) | Subgaussianity, Covering number, bracketing number | VDV Chapter 18-19 |
| Tue, Feb 14 | Lecture 11 (tex) | Symmetrization, Chaining | VDV Chapter 18-19 |
| Thu, Feb 16 | Lecture 12 (tex) | Uniform laws via entropy numbers, classes with finite entropy, VC classes | VDV Chapter 18-19 |
| Tue, Feb 21 | Lecture 13 (tex) | VC classes, general convergence in distribution | VDV Chapter 18-19 |
| Thu, Feb 23 | Lecture 14 (tex) | Equicontinuity, Modulus of continuity for processes | VDV Chapter 18-19 |
| Tue, Feb 28 | Lecture 15 (tex) | Uniform laws via stochastic equicontinuity, M-estimator revisited, Moduli of continuity and rates convergence | VDV Chapter 18-19 |
| Thu, Mar 2 | Lecture 16 (tex) | Moduli of continuity and rates of convergence | VDV Chapter 18-19 |
| Tue, Mar 7 | Lecture 17 (tex) | Asymptotic testing, relative efficiency of tests | VDV Chapter 14 |
| Thu, Mar 9 | Lecture 18 (tex) | Absolute continuity of measure, Contiguity, LeCams's lemmas, exact testing | VDV Chapter 6 |
| Tue, Mar 14 | Lecture 19 (tex) | Quadratic Mean Differentiability, Local Asymptotic Normality | Online notes: contiguity and asymptotics |
| Thu, Mar 16 | Lecture 20 (tex) | Limiting Gaussian experiments, local asymptotic minimax theorem | -
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VDV = van der Vaart (Asymptotic Statistics)
TSH = Testing Statistical Hypotheses
TPE = Theory of Point Estimation
Additional Notes
| Topic | Link |
| Arzela-Ascoli Theorem | pdf |
| VC Dimension | pdf |
| Rates of convergence and moduli of continuity | pdf |
| Contiguity and asymptotics | pdf
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