STAT510: Mathematical Statistics I, Fall 2014
Instructor: Xiaohui Chen (Office: Illini Hall 104A).
Lecture (CL1): MWF 10:00am –10:50am, 165 Everitt Elec & Comp Engr Lab.
Office hours: MW 11:00am –12:00pm, Illini Hall 104A.
Prerequisite: STAT410: Statistics and Probability II.
Announcements:
— Welcome!
— First Day of Class: Aug. 25, 2014, M.
— Last Day of Class: Dec. 10, 2014, W.
— Homework 1 is posted on Compass2g. Due date: 3pm, Tuesday, Sep. 2, 2014.
— Midterm: Wednesday Oct. 8 in class (50 mins). No cheat-sheet and calculator are allowed.
— Last day of withdraw: Oct. 17, 2014, undergraduate deadline to drop without a W; Nov. 14, 2014, graduate deadline to drop without a W.
— Final exam: Friday Dec. 19, 8am-11am, 165 Everitt Elec & Comp Engr Lab (our classroom).
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 Readings
Aug. 25 (M): Introduction
Aug. 27 (W): Probability models
Aug. 29 (F): Method of moments
Week 2 Contents Readings
Sep. 1 (M): Labor Day (no class)
Sep. 3 (W): Maximum likelihood estimation (MLE)
Sep. 5 (F): MLE, profile likelihood, invariance
Week 3 Contents Readings
Sep. 8 (M): Bayes estimation
Sep. 10 (W): Evaluating estimators
Sep. 12 (F): Sufficiency
Week 4 Contents Readings
Sep. 15 (M): Sufficient statistic
Sep. 17 (W): Neyman factorization theorem
Sep. 19 (F): Minimal sufficient statistic
Week 5 Contents Readings
Sep. 22 (M): Exponential and location-scale family
Sep. 24 (W): Fisher information
Sep. 26 (F): Fisher information matrix
Week 6 Contents Readings
Sep. 29 (M): Fisher information matrix, ancillarity
Oct. 1 (W): Ancillary statistic
Oct. 3 (F): Conditional inference, completeness
Week 7 Contents Readings
Oct. 6 (M): Completeness
Oct. 8 (W): Midterm exam (in class)
Oct. 10 (F): Basu’s theorem
Week 8 Contents Readings
Oct. 13 (M): Cramer-Rao lower bound
Oct. 15 (W): Multi-parameter information inequalities
Oct. 17 (F): Rao-Blackwellization
Week 9 Contents Readings
Oct. 20 (M): UMVUE
Oct. 22 (W): Shift equivariance
Oct. 24 (F): Pitman estimator
Week 10 Contents Readings
Oct. 27 (M): Pitman estimator
Oct. 29 (W): General invariance & equivariance
Oct. 31 (F): Invariant groups and equivariant estimators
Week 11 Contents Readings
Nov. 3 (M): Admissibility
Nov. 5 (W): Bayes procedures, minimaxity
Nov. 7 (F): Data reduction principles
Week 12 Contents Readings
Nov. 10 (M): Law of large numbers, consistency
Nov. 12 (W): Weak convergence, continuous mapping
Nov. 14 (F): Central limit theorem (CLT)
Week 13 Contents Readings
Nov. 17 (M): Multivariate CLT, Cramer-Wold device
Nov. 19 (W): Slutsky’s theorem and applications
Nov. 21 (F): Delta-method
Week 14 Contents Readings
Thanksgiving week (no class)
Week 15 Contents Readings
Dec. 1 (M): Multivariate Delta-method
Dec. 3 (W): Consistency of MLE
Dec. 5 (F): Asymptotic normality of MLE
Week 16 Contents Readings
Dec. 8 (M): Asymptotic efficiency of MLE
Dec. 10 (W): Estimation of Poisson model
Final Exam: Friday, Dec. 19, 2014, 8am-11am, 165 Everitt Elec & Comp Engr Lab.