### Syllabus

**Instructor:** Professor Xiao Wang

**Website:** http://www.stat.purdue.edu/~wangxiao/courses/stat528/index.html

**Office:** MATH 514

**Email**: wangxiao@purdue.edu

**Office Hour**: By Appointment Only

**Lecture Time and Location**: Tuesday, Thursday 12:00 pm --- 1:15pm, University 001

Note: Please include “STAT 528” in the subject line when contacting me via email. Due to the large amount of daily emails I receive, your emails may be missed if they do not include “STAT528” in the subject line.

**Grader**: Wei Hao

**E-mail**: haow@purdue.edu

**Required Textbook: **Theoretical Statistics: Topics for a Core Course, by Robert Keener

**Schedule: **Aug 11, 2017—Dec 09, 2017

**Policy**: You are allowed, and even encouraged, to work with other students on the homework problems. Copying of homework, however, is absolutely forbidden and constitutes a violation of the Honor Code; therefore, each student must produce his or her own homework to be handed in and graded. You are also encouraged to ask me or the grader for help on homework problems after you have tried to solve the problems on your own.

**Homework**: Problems will be assigned on each Thursday and due in class on next Thursday. You may drop your homework to the grader’s mail box located at MATH 533 before 10:30 am. Late homework will NOT be accepted. You should contact the grader if you have any questions about grading. Homework will be graded and missed homework will receive a grade of zero. To receive credit on homework you must: show all work neatly, clearly label each problem, circle your final answers, and staple your entire assignment together in the correct order. Solutions will be posted on my website.

**Exam**: There will be one evening midterm and one final. No Makeup Exam unless you have legitimate excuses.

**Final Grade**: Your final grade will depend on the following components with these proportions: homework (30%), midterm (30%), and final exam (40%). The percentage grades needed to achieve an A, B, C, D, or F will follow approximately the following scale: 85 – 100 = A, 70 – 84 = B, 55 – 69 = C, 50 – 54 = D, 0 – 49 = F. This course has "+" and "-" scores.

**Outline: **

- Probability and Measure Ch1
- Basics
- Exponential Family Ch2
- Risk, Sufficiency, completeness, and Ancillary Ch3
- Unbiased Estimator Ch4
- Conditional Distribution Ch6

- Bayesian Estimation
- Bayesian Estimation Ch7
- Bayesian Inference Ch15

- MLE
- A Large Sample Theory Ch8
- Estimating Equations and ML Ch9

- Empirical Bayes and Shrinkage Estimators Ch11
- Hypothesis Testing
- Basic Ch12
- Higher dimension Ch13 (if time permits)
- Likelihood Ratio Test Ch17 (if time permits)