Stats 300B: Theory of Statistics II

John Duchi, Stanford University, Winter 2017

Course Schedule

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

  • 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


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.

Download the LaTeX template and style file for scribing lecture notes.