Stats 300B: Theory of Statistics II
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 5.15.6; ELST Chapter 7.17.3 
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  UStatistics  VDV Chapter 12 
Thu, Feb 1  Lecture 8  UStatistics: 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 1819 
Thu, Feb 15  Lecture 12  Uniform laws via entropy numbers, classes with finite entropy, VC classes  VDV Chapter 1819 
Tue, Feb 20  Lecture 13  Rademacher complexity and ULLNs  VDV Chapter 1819 
Thu, Feb 22  Lecture 14  Moduli of continuity, rates of convergence  VDV Chapter 1819 
Tue, Feb 27  Lecture 15  Weak convergence of random functions  VDV Chapter 1819, Notes on ArzelaAscoli theorem 
Thu, Mar 1  Lecture 16  Goodnessoffit tests, Mestimators with nondifferentiable losses  VDV Chapter 19.3 & 5.3 
Tue, Mar 6    TSH Chapter 12, VDV Chapter 6 
Thu, Mar 8  Lecture 18  Absolute continuity of measure, Contiguity, LeCams's lemmas, Distance for distributions  TSH Chapter 12.3, VDV Chapter 6 
Tue, Mar 13  Lecture 19  Hellinger distance, Quadratic mean differentiability, Local asymptotic normality, Asymptotically most powerful tests  TSH Chapter 12.3, 13.113.3, VDV Chapter 6, 7.17.3 
Thu, Mar 15  Lecture 20  Limiting Gaussian experiments, Local asymptotic minimax theorem  VDV Chapters 7 and 8, Notes on class website

Note: to get the tex for any of the lectures above, simply click the lecture, and in your browser replace the .pdf extension with .tex.
(So, you can get the Lecture 1 pdf and Lecture 1 tex).
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)
All exercises for the class are available at the 2018 exercise list.
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 2017 are available from the 2017 Syllabus. You can download the LaTeX template and style file for scribing lecture notes.
