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


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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.