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 15Lecture 12 Uniform laws via entropy numbers, classes with finite entropy, VC classes VDV Chapter 18-19
Tue, Feb 20Lecture 13 Rademacher complexity and ULLNs VDV Chapter 18-19
Thu, Feb 22Lecture 14 Moduli of continuity, rates of convergence VDV Chapter 18-19
Tue, Feb 27Lecture 15 Weak convergence of random functions VDV Chapter 18-19, Notes on Arzela-Ascoli theorem
Thu, Mar 1Lecture 16 Goodness-of-fit tests, M-estimators with non-differentiable losses VDV Chapter 19.3 & 5.3
Tue, Mar 6 TSH Chapter 12, VDV Chapter 6
Thu, Mar 8Lecture 18 Absolute continuity of measure, Contiguity, LeCams's lemmas, Distance for distributions TSH Chapter 12.3, VDV Chapter 6
Tue, Mar 13Lecture 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 15Lecture 20 Limiting Gaussian experiments, Local asymptotic minimax theorem VDV Chapters 7 and 8, Notes on class website

  • 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
Asymptotics for non-differentiable losses 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.