STAT510: Mathematical Statistics I, Fall 2018
Instructor: Xiaohui Chen (Office: Illini Hall 104A).
Lecture (A1): MWF 10:00am–10:50am,112 Transportation Building.
Office hours: M 1:00pm–3:00pm, Illini Hall 104A.
TA: Tianyi Qu (tianyiq3@illinois.edu).
TA office hours: T 3:00pm — 5:00pm, 104 Illini Hall.
Prerequisite: STAT410: Statistics and Probability II.
Announcements:
— Welcome!
— First Day of Class: Aug. 27, 2018, M.
— Last Day of Class: Dec. 12, 2018, 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. 27 (M): Introduction
Aug. 29 (W): Probability models
Aug. 31 (F): Method of moments
Week 2 Contents
Sep. 3 (M): Labor Day (no class)
Sep. 5 (W): Maximum likelihood estimation (MLE)
Sep. 7 (F): MLE, profile likelihood, invariance
Week 3 Contents
Sep. 10 (M): Bayes estimation
Sep. 12 (W): Evaluating estimators
Sep. 14 (F): Sufficiency
Week 4 Contents
Sep. 17 (M): Sufficient statistic
Sep. 19 (W): Neyman factorization theorem
Sep. 21 (F): Minimal sufficient statistic
Week 5 Contents
Sep. 24 (M): Exponential and location-scale family
Sep. 26 (W): Fisher information
Sep. 28 (F): Fisher information matrix
Week 6 Contents
Oct. 1 (M): Fisher information matrix, ancillarity
Oct. 3 (W): Midterm exam I (in class)
Oct. 5 (F): Ancillary statistic
Week 7 Contents
Oct. 8 (M): Conditional inference, completeness
Oct. 10 (W): Completeness
Oct. 12 (F): Basu’s theorem
Week 8 Contents
Oct. 15 (M): Cramer-Rao lower bound
Oct. 17 (W): Multi-parameter information inequalities
Oct. 19 (F): Rao-Blackwellization
Week 9 Contents
Oct. 22 (M): UMVUE
Oct. 24 (W): Shift equivariance
Oct. 26 (F): Pitman estimator
Week 10 Contents
Oct. 29 (M): Pitman estimator
Oct. 31 (W): General invariance & equivariance
Nov. 2 (F): Midterm exam II (in class)
Week 11 Contents
Nov. 5 (M): Invariant groups and equivariant estimators
Nov. 7 (W): Admissibility
Nov. 9 (F): Bayes procedures, minimaxity
Week 12 Contents
Nov. 12 (M): Law of large numbers, consistency
Nov. 14 (W): Weak convergence, continuous mapping
Nov. 16 (F): Central limit theorem (CLT)
Week 13 Contents
Thanksgiving week (no class)
Week 14 Contents
Nov. 26 (M): Multivariate CLT, Cramer-Wold device
Nov. 28 (W): Slutsky’s theorem and applications
Nov. 30 (F): Delta-method
Week 15 Contents
Dec. 3 (M): Multivariate Delta-method
Dec. 5 (W): Consistency of MLE
Dec. 7 (F): Asymptotic normality of MLE
Week 16 Contents
Dec. 10 (M): Asymptotic efficiency of MLE
Dec. 12 (W): Estimation of Poisson model
Final Exam: 1:30-4:30 p.m., Monday, Dec. 17 @ 112 Transportation Building (classroom).