Courses

STAT 620 Asymptotic Statistics

View Lecture Notes (27 lectures)
Lecture NotesTopics
Lecture 1review of probability theory
Lecture 2review of probability theory
Lecture 3CLT, first-order delta method
Lecture 4variance stabilizing transformation, second-order delta method
Lecture 5moment estimators, Taylor expansions
Lecture 6maximum likelihood estimation
Lecture 7asymptotic normality, efficiency
Lecture 8exponential family, ARE, super efficiency
Lecture 9testing & confidence sets
Lecture 10testing a subvector, definition of U-statistics
Lecture 11examples of U-statistics, variance of U-statistics
Lecture 12Hajek projection
Lecture 13Hajek projection
Lecture 14metric entropy, bracketing, uniform laws of large numbers
Lecture 15Sub-Gaussianity, Hoeffding's inequality
Lecture 16Symmetrization
Lecture 17McDiarmid's inequality
Lecture 18Sub-Gaussian process, Dudley's integral entropy
Lecture 19Lipschitz functions, VC dimension
Lecture 20VC dimension
Lecture 21Convergence rate, Some concepts of convergence in distribution
Lecture 22Asymptotically equicontinuous
Lecture 23Donsker Class, Goodness of fit statistics
Lecture 24Functional delta method
Lecture 25Bootstrap, Gaussian sequence model
Lecture 26Soft/hard-thresholding estimators, risk inflation
Lecture 27Lasso consistency

STAT 689 Large-scale and high-dimensional statistical inference

View Lecture Notes (15 lectures)
Lecture NotesTopics
Lecture 1Testing the global null, Bonferroni's test
Lecture 2Fisher's combination test
Lecture 3Simes test, Goodness of fit tests, Higher-criticism test
Lecture 4FWER controlling procedures, Closure principle
Lecture 5Graphical procedures
Lecture 6False discovery rate, BH procedure, Barber and Candès procedure
Lecture 7PRDS property
Lecture 8Empirical process viewpoint, Bayesian viewpoint, Positive false discovery rate and q-values
Lecture 9E-values
Lecture 10: Part IConditional randomization tests, Knockoff filter
Lecture 10: Part IIKnockoff filter
Lecture 11Conformal prediction
Lecture 12Debiased Lasso
Lecture 13Selective inference
Lecture 14Selective inference
Lecture 15Applications to LLMs