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

**Location (in person and on campus):**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 or by appointment**Textbook (required):**R. V. Hogg, J. W. McKean, A. T. Craig,*Introduction to Mathematical Statistics*, 8th edition, 2019

**Reference Books (optional):**- 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.

**Course Description:**STAT 411. Statistical Theory. Estimation, tests of statistical hypotheses, best tests, sufficient statistics, Rao-Cramer inequality, sequential probability ratio tests, the multivariate normal distribution, nonparametric methods.

**Course Credits:**3 hours for undergraduates or 4 hours for graduate students.

**Prerequisite:**Grade of C or better in STAT 401.

**Course Goals:**Understand fundamental concepts and principles of mathematical statistics; construct and formulate efficient estimators and powerful hypothesis tests for statistical models.

**Learning Objectives:**Understand and calculate maximum likelihood estimation, Rao-Cramer lower bound, and efficiency; understand sufficiency, completeness, and exponential class of distributions; construct minimum variance unbiased estimators; understand likelihood ratio tests and construct most powerful tests; understand Bayesian statistics

**Attendance/Participation Policy:**Students are expected to attend the lectures and participate in the discussions. Attendance will be counted at least six times during the course period and the students who present may receive half credit point each time and up to three extra credit points in total on the final grade at a 100-point scale. Students who actively participate in the discussion may receive half or one credit point each time and up to five credit points in total. If for any reason you could not present in class on time, please send me an email at your earliest convenience. If you need special accommodations due to disabilities, please contact the Disability Resource Center for a Letter of Accommodation (LOA).

**Assignments, Due Dates, and Deadlines:**Homework will be assigned at a weekly basis; turn in your homework 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

**Policy for Missed or Late Homework:**Students may request up to two days' extension for each homework; late homework without request ahead of time or longer than two days will not be accepted; the lowest two homework scores will be dropped for final grade.

**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
## Community Agreement/Classroom Conduct Policy

- Be present by turning off cell phones and removing yourself from other distractions.

- Be respectful of the learning space and community. For example, no side conversations or unnecessary disruptions.

- Use preferred names and gender pronouns.

- Assume goodwill in all interactions, even in disagreement.

- Facilitate dialogue and value the free and safe exchange of ideas.

- Try not to make assumptions, have an open mind, seek to understand, and not judge.

- Approach discussion, challenges, and different perspectives as an opportunity to think out loud, learn something new, and understand the concepts or experiences that guide other people's thinking.

- Debate the concepts, not the person.

- Be gracious and open to change when your ideas, arguments, or positions do not work or are proven wrong.

- Be willing to work together and share helpful study strategies.

- Be mindful of one another's privacy, and do not invite outsiders into our classroom.

- Be present by turning off cell phones and removing yourself from other distractions.
## 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.

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