Stats 300B: Theory of Statistics II
Course Schedule (subject to change)
 Lecture Notes  Topics  Reading 
Tue, Jan 8  Lecture 1  Overview, Convergence of random variables  VDV Chapters 2.1, 2.2 
Thu, Jan 10  Lecture 2  Convergence of random variables, delta method  VDV Chapters 2, 3 
Tue, Jan 15  Lecture 3  Asymptotic normality, Fisher information  VDV Chapter 5.15.6; ELST Chapter 7.17.3 
Thu, Jan 17  Lecture 4  Fisher information, Moment method  VDV Chapter 4; TPE Chapter 2.5 
Tue, Jan 22  Lecture 5  Superefficiency, Testing and Confidence Regions  ELST Chapter 3.1, 3.2, 4.1; TSH Chapter 12.4 
Thu, Jan 24  Lecture 6  Testing: likelihood ratio, Wald, Score tests  ELST Chapter 3.1, 3.2, 4.1; TSH Chapter 12.4 
Tue, Jan 29  Lecture 7  UStatistics  VDV Chapter 12 
Thu, Jan 31  Lecture 8  UStatistics: Hajek projections and asymptotic normality  VDV Chapter 11, 12 
Tue, Feb 5  Lecture 9  Uniform laws of large numbers, Covering and Bracketing  VDV Chapter 5.2, 19.1, 19.2 
Thu, Feb 7  Lecture 10  Subgaussianity, Symmetrization, Rademacher complexity and metric entropy  VDV Chapter 19, HDP Chapter 1, 2, 8 
Tue, Feb 12  Lecture 11  Symmetrization, Chaining  HDP Chapter 8, VDV Chapter 1819 
Thu, Feb 14  Lecture 12  Uniform laws via entropy numbers, classes with finite entropy, VC classes  VDV Chapter 1819 
Tue, Feb 19  Lecture 13  Rademacher complexity and ULLNs  VDV Chapter 1819 
Thu, Feb 21  Lecture 14  Moduli of continuity, rates of convergence, Gaussian sequence model  VDV Chapter 1819, GE Chapter 1 
Tue, Feb 26  Lecture 15  Gaussian sequence model, hard and soft thresholding  GE Chapter 2 
Thu, Feb 28  Lecture 16  Incoherent matrices and concentration inequalities, LASSO  HDP Chapter 23 
Tue, Mar 5  Lecture 17  Lasso and Highdimensional Regression, Generic Chaining  HDP 10.510.6, HDP 8.5 
Thu, Mar 7  Lecture 18  Generic Chaining, Comparison Inequality  HDP 8.6, 9.19.2 
Tue, Mar 12  Lecture 19  Restricted strong convexity and matrix deviation  HDP 9.1 
Thu, Mar 14   Review 

VDV = van der Vaart (Asymptotic Statistics)
HDP = Vershynin (High Dimensional Probability)
TSH = Testing Statistical Hypotheses (Lehmann and Romano)
TPE = Theory of Point Estimation (Lehmann)
ELST = Elements of Large Sample Theory (Lehmann)
GE = Gaussian estimation: Sequence and wavelet models (Johnstone)
Additional Notes
Topic  Link 
ArzelaAscoli Theorem  pdf 
VC Dimension  pdf 
Rates of convergence and moduli of continuity  pdf 
Asymptotics for nondifferentiable losses  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 2018 are available from the 2018 Syllabus. You can download the LaTeX template and style file for scribing lecture notes.
