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.