STATS 200C: Large Sample Theory
Prerequiste: STATS 200A and B
Law of large number (L2 and L1 versions)
Central limit theorem (Characteristic function, Linderberg, Stein)
Large deviation and concentration inequalities (Chernoff, Cramer, Hoeffding, Benett, Bernstein)
Asymptotics of maximum likelihood and M-estimators, likelihood ratio test
Many means problem, minimax, Pinsker bound, Stein estimator, soft thresholding, oracle inequalities, theory of Lasso etc.
Supervised learning, VC dimension, Rademacher complexity, theories of SVM and adaboost.