**Course Announcement****Time:**Monday, Wednesday, Friday at 10:00 - 10:50 a.m.

**Location:**Lecture Center Building A (805 S Morgan St, Chicago, IL 60607), Room A003**Instructor:**Jie Yang

**Office:**SEO 513

**Phone:**(312) 413-3748

**E-Mail:**jyang06 AT uic DOT edu

**Office Hours:**Monday, Wednesday, Friday at 11:00 a.m. - 12:00 p.m. at UIC Zoom**Textbook:**R. V. Hogg, J. W. McKean, A. T. Craig,*Introduction to Mathematical Statistics*, 8th edition, 2019

**Reference Books:**- Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman,
*Probability and Statistical Inference*, 10th Edition, 2020.

- Kandethody M. Ramachandran, Chris P. Tsokos,
*Mathematical Statistics with Applications in R*, 3rd Edition, 2020.

**Content:**Maximum likelihood estimation, Rao-Cramer lower bound and efficiency, sufficient statistic and completeness, exponential class of distributions, most powerful test, likelihood ratio test, Bayesian statistics

**Prerequisite:**Grade of C or better in STAT 401**Homework:**Turn in every Wednesday before class via UIC Blackboard; half of the grade counts for completeness; half of the grade counts for correctness of one selected problem

**Exams:**This course will require students to be on campus for in-person exams on September 29th (Friday) and November 10th (Friday), 10:00 AM - 10:50 AM.

**Project:**Students are required to work by themselves or in groups on course projects and submit their final reports before December 1st, 2023, Friday, 10:00am. Each group should consist of at most three students. The projects may come from the optional problems assigned by the instructor or be proposed by the students themselves upon the approval of the instructor.

**Grading:**Homework 20%, Two Exams 25% each, Project 30%

**Grading Scale:**90% A , 80% B , 70% C , 60% D**Format of All Exams:**Each exam is based on the homework and the examples discussed in class. The last class session before each exam is a review session. Please prepare any questions that you may have.*No makeup exam will be given without a valid excuse*.

- Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman,
**Course Syllabus**

**WEEK****SECTIONS****BRIEF DESCRIPTION**08/21 - 08/25 3.1, 3.2, 3.3; 3.4, 3.5, 3.6; 4.1, 4.2, 4.4 Review on Special Distributions; Sampling and Statistics, Confidence Interval, Order Statistics 08/28 - 09/01 5.3; 6.1; 6.1 Central Limit Theorem; Maximum Likelihood Estimation 09/04 - 09/08 Holiday; 6.2; 6.2 Rao-Cramer Lower Bound and Efficiency 09/11 - 09/15 6.3; 6.3; 6.4 Maximum Likelihood Tests; Multiparameter Case: Estimation 09/18 - 09/22 6.4; 7.1; 7.1 Multiparameter Case: Estimation; Measures of Quality of Estimators 09/25 - 09/29 7.1; Review; **Exam-I**Measures of Quality of Estimators 10/02 - 10/06 7.2; 7.2; 7.3 A Sufficient Statistic for a Parameter; Properties of a Sufficient Statistic 10/09 - 10/13 7.4; 7.5; 7.5 Completeness and Uniqueness; The Exponential Class of Distributions 10/16 - 10/20 7.7; 7.7; 7.8 The Case of Several Parameters; Minimal Sufficiency and Ancillary Statistics 10/23 - 10/27 7.8; 7.9; 7.9 Minimal Sufficiency and Ancillary Statistics; Sufficiency, Completeness and Independence 10/30 - 11/03 8.1; 8.1; 8.2 Most Powerful Tests; Uniformly Most Powerful Tests 11/06 - 11/10 8.2; Review; **Exam-II**Uniformly Most Powerful Tests 11/13 - 11/17 8.2; 8.3; 8.3 Uniformly Most Powerful Tests; Likelihood Ratio Tests 11/20 - 11/24 11.1; 11.1; Holiday Likelihood Ratio Tests; Bayesian Procedures 11/27 - 12/01 11.1; 11.3; 11.4 Bayesian Procedures; Gibbs Sampler; Modern Bayesian Methods

**Homework**- Homework #1, due 08/30/2023

- Homework #2, due 09/06/2023

- Homework #3, due 09/13/2023

- Homework #4, due 09/20/2023

- Homework #5, due 09/27/2023

- Homework #6, due 10/11/2023

- Homework #7, due 10/18/2023

- Homework #8, due 10/25/2023

- Homework #9, due 11/01/2023

- Homework #10, due 11/08/2023

- Homework #11, due 11/22/2023

- Homework #12, due 11/29/2023

- Homework #1, due 08/30/2023
**Handout**- Mathematical Symbols
- Derivatives, Integrals and Series
- Power Series
- Table I: Poisson Distribution
- Table III: Normal Distribution

**Using R**- Download
**R**for Free -- the most popular software used by statisticians

- Learn R in 15 Minutes

- Use R to Compute Numerical Integrals

- RStudio -- a convenient set of integrated tools for R, including programming, plotting, and workspace management

- Downloadable Books on R:
*An Introduction to R*, by William N. Venables, David M. Smith and the R Development Core Team

*Using R for Data Analysis and Graphics - Introduction, Code and Commentary*, by John H. Maindonald

**More R Books in Different Languages ...**

- R Code for the Course:

- Download
**Relevant Course Materials**- Textbook Web Page -- including Errata page and R code

- R. A. Fisher and the Making of Maximum Likelihood (for §6.1)

- Interchange of Differentiation and Integration (for §6.2)

- Factorization Theorem for Determining a Sufficient Statistic (for §7.2)

- Textbook Web Page -- including Errata page and R code
## Disability Accommodations Statement

UIC is committed to full inclusion and participation of people with disabilities in all aspects of university life. Students who face or anticipate disability-related barriers while at UIC should connect with the Disability Resource Center (DRC) at drc.uic.edu, drc@uic.edu, or at (312) 413-2183 to create a plan for reasonable accommodations. In order to receive accommodations, students must disclose disability to the DRC, complete an interactive registration process with the DRC, and provide their course instructor with a Letter of Accommodation (LOA). Course instructors in receipt of an LOA will work with the student and the DRC to implement approved accommodations.

UIC Home | Library | MSCS | Jie's Home