Stats 300B: Theory of Statistics II

John Duchi, Stanford University, Winter 2018

Course Schedule

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