STAT575

STAT575 / ECON578: Large Sample Theory, Spring 2017

Instructor: Xiaohui Chen (Office:104A Illini Hall).
Lecture (A1): TR 9:30am — 10:50am, 207 Gregory Hall.
Office Hours: TR 2:00pm — 3:00pm, 104A Illini Hall.
Course TA: Chung Eun Lee (clee135@illinois.edu).
TA Office Hours: Wednesday 2-4pm,122 Illini Hall, conference room; OR by appointment.

Syllabus

Required TextA Course in Large Sample Theory. Thomas S Ferguson. Chapman & Hall/CRC Texts in Statistical Science. First Edition 1996.
References:
— E.L. Lehmann. (1999) Elements of Large-Sample Theory. Springer.
— A.W. van der Vaart. (2000) Asymptotic Statistics. Cambridge.
— A. Dasgupta. (2008) Asymptotic Theory of Statistics and Probability. Springer.
Prerequisite:
(i) STAT511 Mathematical Statistics II.
(ii) STAT553 Probability and Measure I or MATH561 Theory of Probability I.

Announcements:
— Welcome!
— First Day of Class: Jan. 17, 2017, T.
Last Day of Class: May 2, 2017, T.

Course Plan/Progress (Tentative)

Week 1                                               Contents
Jan. 17 (T):                   Introduction and review of convergence concepts
Jan. 19 (R):             Review of measure theory and convergence diagram

Week 2                                               Contents
Jan. 24 (T):            Partial converse of convergence diagram, Scheffe’s lemma
Jan. 26 (R):                Convergence in distribution, portmanteau theorem

Week 3                                               Contents
Jan. 31 (T):                                          Slutsky lemma
Feb. 2 (R):                           Law of large numbers, Glivenko-Cantelli

Week 4                                               Contents
Feb. 7 (T):                          Central limit theorem, Lindeberg-Feller
Feb. 9 (R):                        Berry-Esseen, Edgeworth expansion

Week 5                                               Contents
Feb. 14 (T):                                    Delta method I
Feb. 16 (R):                                   Delta method II

Week 6                                               Contents
Feb. 21 (T):                         Strong consistency of sample quantiles
Feb. 23 (R):                     Asymptotic distribution of sample quantiles

Week 7                                               Contents
Feb. 28 (T):                            L-estimation, Bahadur representation
Mar. 2 (R):                                  Projection, U-statistics

Week 8                                               Contents
Mar. 7 (T):                                            Midterm
Mar. 9 (R):                     Degeneracy, Hoeffding decomposition

Week 9                                               Contents
Mar. 14 (T):                         Stationary m-dependent sequence
Mar. 16 (R):                  WLLN, CLT for dependent random variables

Week 10                                               Contents

                                                Spring vacation, no class

Week 11                                               Contents
Mar. 28 (T):                     Cramer-von Mises functionals, V-statistics
Mar. 30 (R):                 Continuity of statistical functionals, influence function

Week 12                                               Contents
Apr. 4 (T):                                Functional Delta method
Apr. 6 (R):                    Limiting distribution of statistical functionals

Week 13                                               Contents
Apr. 11 (T):                                            Bootstrap I
Apr. 13 (R):                                           Bootstrap II

Week 14                                               Contents
Apr. 18 (T):                     M-estimation, uniform law of large numbers
Apr. 20 (R):               Strong consistency of MLE, Shannon-Kolmogorov inequality

Week 15                                               Contents
Apr. 25 (T):                              Asymptotic normality of MLE
Apr. 27 (R):                   Cramer-Rao lower bound, asymptotic efficiency

Week 16                                               Contents
May. 2 (T):                       Hodges’ super-efficiency, method of scoring

Final Exam: May 9, 2017 (Tuesday), 7:00pm — 10:00pm, 207 Gregory Hall.