Stats 300B: Theory of Statistics II
Course Schedule (subject to change)
| Lecture Notes | Topics | Reading |
| Tue, Jan 9 | Lecture 1 | Overview, Convergence of random variables | VDV Chapters 2.1, 2.2 |
| Thu, Jan 11 | Lecture 2 | Convergence of random variables, delta method | VDV Chapters 2, 3 |
| Tue, Jan 16 | Lecture 3 | Asymptotic normality, Fisher information | VDV Chapter 5.1-5.6; ELST Chapter 7.1-7.3 |
| Thu, Jan 18 | Lecture 4 | Fisher information, Moment method | VDV Chapter 4; TPE Chapter 2.5 |
| Tue, Jan 23 | Lecture 5 | Superefficiency, Testing and Confidence Regions | ELST Chapter 3.1, 3.2, 4.1; TSH Chapter 12.4 |
| Thu, Jan 25 | Lecture 6 | Testing: likelihood ratio, Wald, Score tests | ELST Chapter 3.1, 3.2, 4.1; TSH Chapter 12.4 |
| Tue, Jan 30 | Lecture 7 | U-Statistics | VDV Chapter 12 |
| Thu, Feb 1 | Lecture 8 | U-Statistics: Hajek projections and asymptotic normality | VDV Chapter 11, 12 |
| Tue, Feb 6 | Lecture 9 | Uniform laws of large numbers, Covering and Bracketing | VDV Chapter 5.2, 19.1, 19.2 |
| Thu, Feb 8 | Lecture 10 | Subgaussianity, Symmetrization, Rademacher complexity and metric entropy | VDV Chapter 19, HDP Chapter 1, 2, 8 |
| Tue, Feb 13 | Lecture 11 | Symmetrization, Chaining | HDP Chapter 8, VDV Chapter 18-19 |
| Thu, Feb 15 | Lecture 12 | Uniform laws via entropy numbers, classes with finite entropy, VC classes | VDV Chapter 18-19 |
| Tue, Feb 20 | Lecture 13 | Rademacher complexity and ULLNs | VDV Chapter 18-19 |
| Thu, Feb 22 | Lecture 14 | Moduli of continuity, rates of convergence | VDV Chapter 18-19 |
| Tue, Feb 27 | Lecture 15 | Weak convergence of random functions | VDV Chapter 18-19, Notes on Arzela-Ascoli theorem |
| Thu, Mar 1 | Lecture 16 | Goodness-of-fit tests, M-estimators with non-differentiable losses | VDV Chapter 19.3 & 5.3 |
| Tue, Mar 6 | | Quadratic-mean differentiability | TSH Chapter 12, VDV Chapter 6 |
| Thu, Mar 8 | Lecture 18 | Absolute continuity of measure, Contiguity, LeCams's lemmas, Distance for distributions | TSH Chapter 12.3, VDV Chapter 6 |
| Tue, Mar 13 | Lecture 19 | Hellinger distance, Quadratic mean differentiability, Local asymptotic normality, Asymptotically most powerful tests | TSH Chapter 12.3, 13.1-13.3, VDV Chapter 6, 7.1-7.3 |
| Thu, Mar 15 | Lecture 20 | Limiting Gaussian experiments, Local asymptotic minimax theorem | VDV Chapters 7 and 8, Notes on class website
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Note: to get the tex for any of the lectures above, simply click the lecture, and in your browser replace the .pdf extension with .tex.
(So, you can get the Lecture 1 pdf and Lecture 1 tex).
VDV = van der Vaart (Asymptotic Statistics)
HDP = Vershynin (High Dimensional Probability)
TSH = Testing Statistical Hypotheses (Lehmann and Romano)
TPE = Theory of Point Estimation
HDS = Wainwright (High Dimensional Statistics: A Non-Asymptotic Viewpoint)
ELST = Elements of Large Sample Theory (Lehmann)
All exercises for the class are available at the 2018 exercise list.
Additional Notes
| Topic | Link |
| Arzela-Ascoli Theorem | pdf |
| VC Dimension | pdf |
| Rates of convergence and moduli of continuity | pdf |
| Asymptotics for non-differentiable losses | pdf |
| Contiguity and asymptotics | pdf
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Scribing
The scribe notes should be written in prose English, as if in a
textbook, so that someone who did not attend the class will understand
the material. Please do your best, as it is good practice for
communicating with others when you write research papers.
Here is the Scribing Schedule.
All tex files and scribe notes from 2017, 2018, and 2019 are available
from their respective syllabi (2017,
2018, 2019). You can
download the LaTeX template and
style file for scribing lecture notes.
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