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   Uniform laws via entropy numbers, classes with finite entropy, VC classes  VDV Chapter 1819 
Tue, Feb 20   Rademacher complexity and ULLNs  
Thu, Feb 22   Moduli of continuity, rates of convergence  VDV Chapter 1819 
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 78 
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 
ArzelaAscoli Theorem  pdf 
VC Dimension  pdf 
Rates of convergence and moduli of continuity  pdf 
Contiguity and asymptotics  pdf

Scribing
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