Stats 300B: Theory of Statistics II

John Duchi, Stanford University, Winter 2018

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 Uniform laws via entropy numbers, classes with finite entropy, VC classes VDV Chapter 18-19
Tue, Feb 20 Rademacher complexity and ULLNs
Thu, Feb 22 Moduli of continuity, rates of convergence VDV Chapter 18-19
Tue, Feb 27 Matrix concentration HDP Chapter 4
Thu, Mar 1 Asymptotic testing, relative efficiency of tests TSH Chapter 12, VDV Chapter 14
Tue, Mar 6 Absolute continuity of measure, Contiguity, LeCams's lemmas, exact testing TSH Chapter 12, VDV Chapter 6
Thu, Mar 8 Quadratic Mean Differentiability, Local Asymptotic Normality VDV Chapter 7, Online notes: contiguity and asymptotics
Tue, Mar 13 Limiting Gaussian experiments, local asymptotic minimax theorem VDV Chapter 7-8
Thu, Mar 15 Review and perspective -


  • VDV = van der Vaart (Asymptotic Statistics)

  • HDP = Vershynin (High Dimensional Probability)

  • TSH = Testing Statistical Hypotheses (Lehmann and Romano)

  • TPE = Theory of Point Estimation

  • ELST = Elements of Large Sample Theory (Lehmann)

Additional Notes

Topic Link
Arzela-Ascoli Theorem pdf
VC Dimension pdf
Rates of convergence and moduli of continuity 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 2017 are available from the 2017 Syllabus. You can download the LaTeX template and style file for scribing lecture notes.