SDS 384-11:Theoretical Statistics
While measure theory is not a pre-requisite for this class, you can use Peter Hoff's notes on measure theory if needed. Another excellent reference is ``Probability and Measure''
01/15,17 : Syllabus [PDF] , and stochastic convergence [Slides].
01/12,17 : More stochastic convergence [Slides]. Chapter 2 Van-der-vaart
01/31, 2/1 : Concentration inequalities I (Markov, Chebychev, Hoeffding's Lemma, SubGaussian RVs) [Slides].
02/1 : Concentration inequalities II (Subexponential RV's, JL Lemma) [Slides].
02/1,6 : Concentration inequalities III (Martingales, Azuma-Hoeffding, McDiarmid's inequality) [Slides].
02/6,8 : Concentration inequalities III (The Gaussian Lipschitz theorem) [Slides].
02/13,18 : Concentration inequalities IV (Talagrand's inequality) [Slides].
Reading : Terry Tao's notes for Talagrand's inequality [Here].
Reading : The USVT paper by Sourav Chatterjee [Here].
02/20 : Efron-Stein inequality [Slides].
Reading : Chapter 4 from Gabor Lugosi's notes [here].
02/23 : U statistics (definitions, concentration) [Slides].
03/2 : Reading: how it all started. [Paul Halmos's 1946 paper].
02/25 : U statistics cont. (variance calculation, examples) [Slides].
03/2 : U statistics cont. (Normal convergence) [Slides].
03/7 : Uniform Law of Large Numbers (Intro) [here].
03/9 : Uniform Law of Large Numbers II (Symmetrization, Rademacher complexity) [here].
Reading : Martin's book chapter 4 and 5
04/3 : Uniform Law of Large Numbers III (VC dimension, Sauer's Lemma) [here].
04/3 : Uniform Law of Large Numbers IV (Covering number, packing number) [here].
04/8,10 : Uniform Law of Large Numbers V (Example: operator norm) [here].
04/10,15 : Uniform Law of Large Numbers VI (Stochastic processes and covering numbers) [here].
04/27 : Uniform Law of Large Numbers VII (Dudley's chaining) [here].
04/15 : Concentration of vectors and matrices [here].
04/30, 5/1 : Covariance estimation [here].