STAT510: Mathematical Statistics I, Fall 2017
Instructor: Xiaohui Chen (Office: Illini Hall 104A).
Lecture (A1): MWF 10:00am–10:50am,112 Transportation Building.
Office hours: WF 11:00am–12:00pm, Illini Hall 104A.
TA: Changbo Zhu (changbo2@illinois.edu).
TA office hours:
— Tuesday 3pm–4pm, 122 Illini Hall, conference room.
— Thursday 5pm–6pm, 122 Illini Hall, conference room.
Prerequisite: STAT410: Statistics and Probability II.
Announcements:
— Welcome!
— First Day of Class: Aug. 28, 2017, M.
— Last Day of Class: Dec. 13, 2017, W.
Required Text:
— George Casella and Roger L. Berger. Statistical Inference. Second Edition. Duxbury. Thomson Learning.
— John Marden. Mathematical Statistics: Old School. Download
Course Plan/Progress (Tentative)
Week 1 Contents
Aug. 28 (M): Introduction
Aug. 30 (W): Probability models
Sep. 1 (F): Method of moments
Week 2 Contents
Sep. 4 (M): Labor Day (no class)
Sep. 6 (W): Maximum likelihood estimation (MLE)
Sep. 8 (F): MLE, profile likelihood, invariance
Week 3 Contents
Sep. 11 (M): Bayes estimation
Sep. 13 (W): Evaluating estimators
Sep. 15 (F): Sufficiency
Week 4 Contents
Sep. 18 (M): Sufficient statistic
Sep. 20 (W): Neyman factorization theorem
Sep. 22 (F): Minimal sufficient statistic
Week 5 Contents
Sep. 25 (M): Exponential and location-scale family
Sep. 27 (W): Fisher information
Sep. 29 (F): Fisher information matrix
Week 6 Contents
Oct. 2 (M): Fisher information matrix, ancillarity
Oct. 4 (W): Ancillary statistic
Oct. 6 (F): Conditional inference, completeness
Week 7 Contents
Oct. 9 (M): Completeness
Oct. 11 (W): Basu’s theorem
Oct. 13 (F): Midterm exam (in class)
Week 8 Contents
Oct. 16 (M): Cramer-Rao lower bound
Oct. 18 (W): Multi-parameter information inequalities
Oct. 20 (F): Rao-Blackwellization
Week 9 Contents
Oct. 23 (M): UMVUE
Oct. 25 (W): Shift equivariance
Oct. 27 (F): Pitman estimator
Week 10 Contents
Oct. 30 (M): Pitman estimator
Nov. 1 (W): General invariance & equivariance
Nov. 3 (F): Invariant groups and equivariant estimators
Week 11 Contents
Nov. 6 (M): Admissibility
Nov. 8 (W): Bayes procedures, minimaxity
Nov. 10 (F): Data reduction principles
Week 12 Contents
Nov. 13 (M): Law of large numbers, consistency
Nov. 15 (W): Weak convergence, continuous mapping
Nov. 17 (F): Central limit theorem (CLT)
Week 13 Contents
Thanksgiving week (no class)
Week 14 Contents
Nov. 27 (M): Multivariate CLT, Cramer-Wold device
Nov. 29 (W): Slutsky’s theorem and applications
Dec. 1 (F): Delta-method
Week 15 Contents
Dec. 4 (M): Multivariate Delta-method
Dec. 6 (W): Consistency of MLE
Dec. 8 (F): Asymptotic normality of MLE
Week 16 Contents
Dec. 11 (M): Asymptotic efficiency of MLE
Dec. 13 (W): Estimation of Poisson model
Final Exam: Monday, Dec. 18, 2017, 7:00pm-10:00pm, 112 Transportation Building.