Stats 300B: Theory of Statistics II
Course Schedule (subject to change)
| Lecture Notes | Topics | Reading |
| Tue, Jan 8 | Lecture 1 | Overview, Convergence of random variables | VDV Chapters 2.1, 2.2 |
| Thu, Jan 10 | Lecture 2 | Convergence of random variables, delta method | VDV Chapters 2, 3 |
| Tue, Jan 15 | Lecture 3 | Asymptotic normality, Fisher information | VDV Chapter 5.1-5.6; ELST Chapter 7.1-7.3 |
| Thu, Jan 17 | Lecture 4 | Fisher information, Moment method | VDV Chapter 4; TPE Chapter 2.5 |
| Tue, Jan 22 | Lecture 5 | Superefficiency, Testing and Confidence Regions | ELST Chapter 3.1, 3.2, 4.1; TSH Chapter 12.4 |
| Thu, Jan 24 | Lecture 6 | Testing: likelihood ratio, Wald, Score tests | ELST Chapter 3.1, 3.2, 4.1; TSH Chapter 12.4 |
| Tue, Jan 29 | Lecture 7 | U-Statistics | VDV Chapter 12 |
| Thu, Jan 31 | Lecture 8 | U-Statistics: Hajek projections and asymptotic normality | VDV Chapter 11, 12 |
| Tue, Feb 5 | Lecture 9 | Uniform laws of large numbers, Covering and Bracketing | VDV Chapter 5.2, 19.1, 19.2 |
| Thu, Feb 7 | Lecture 10 | Subgaussianity, Symmetrization, Rademacher complexity and metric entropy | VDV Chapter 19, HDP Chapter 1, 2, 8 |
| Tue, Feb 12 | Lecture 11 | Symmetrization, Chaining | HDP Chapter 8, VDV Chapter 18-19 |
| Thu, Feb 14 | Lecture 12 | Uniform laws via entropy numbers, classes with finite entropy, VC classes | VDV Chapter 18-19 |
| Tue, Feb 19 | Lecture 13 | Rademacher complexity and ULLNs | VDV Chapter 18-19 |
| Thu, Feb 21 | Lecture 14 | Moduli of continuity, rates of convergence, Gaussian sequence model | VDV Chapter 18-19, GE Chapter 1 |
| Tue, Feb 26 | Lecture 15 | Gaussian sequence model, hard and soft thresholding | GE Chapter 2 |
| Thu, Feb 28 | Lecture 16 | Incoherent matrices and concentration inequalities, LASSO | HDP Chapter 2-3 |
| Tue, Mar 5 | Lecture 17 | Lasso and High-dimensional Regression, Generic Chaining | HDP 10.5-10.6, HDP 8.5 |
| Thu, Mar 7 | Lecture 18 | Generic Chaining, Comparison Inequality | HDP 8.6, 9.1-9.2 |
| Tue, Mar 12 | Lecture 19 | Restricted strong convexity and matrix deviation | HDP 9.1 |
| Thu, Mar 14 | | Review |
|
VDV = van der Vaart (Asymptotic Statistics)
HDP = Vershynin (High Dimensional Probability)
TSH = Testing Statistical Hypotheses (Lehmann and Romano)
TPE = Theory of Point Estimation (Lehmann)
ELST = Elements of Large Sample Theory (Lehmann)
GE = Gaussian estimation: Sequence and wavelet models (Johnstone)
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
|
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 2018 are available from the 2018 Syllabus. You can download the LaTeX template and style file for scribing lecture notes.
|