STAT510

STAT510: Mathematical Statistics I, Fall 2014

InstructorXiaohui 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.

Syllabus

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.