An introductory graduate level course. This is the first part of one-year series course in mathematical statistics for Ph.D. students in statistics. Math 5061-5062 will provide students with a rigorous introduction to probability theory and an overview of finite sample and large sample theory in statistics.
Instructor: Jimin Ding;
Office Hours:
Wed. 3-4pm. or by appointment
Topics covered:
- Probability spaces; derivation and transformation of probability distributions; generating functions and characteristic functions; law of large numbers, central limit theorem; exponential family; sufficiency, uniformly minimum variance unbiased estimators, Rao-Blackwell theorem, information inequality; maximum likelihood estimation; estimating equation; Bayesian estimation; minimax estimation; basics of decision theory.
Prerequisites:
Math 4111(Analysis)-4121(Introduction to Lebesgue Integration) or the equivalent, or permission of instructor.
Textbook:
Jun Shao,
Mathematical Statistics, 2nd edition
Springer, 2003, ISBN 0-387-95382-5
Exams:
Midterm: Oct.12 (Thur).
Final: Dec. 12 (Tue) 10-12pm. -- Temporal
Both midterm and final will be in-class closing-books-and-notes exams. You may take no more than 1 page (letter size, double-sided) sheet.
Homeworks:
There will be 11 homework assignments throughout the semester.The lowest homework grade will be dropped. About 4 homework problems
will be assigned each week and collected on Thursday. Solutions should be written up neatly and independently. You are encouraged (but not required) to type them in LaTex. Late homework will only be accepted within 48 hours of due time and the grade will be scaled by 70% as a penalty.
Make a copy of each homework before you hand it in !!
It may not be returned before you need to refer to it for the next
homework (or for the next test).
Grades:
Grades will be based on the homework sets (around 50%), on the midterm (around 20%) and on the final (around 25%).
Collaboration:
Collaboration on homework is allowed and can be helpful (and fun). However, you must do all written work by yourself, both answers to homework questions and computer programs. If you collaborate with someone on a homework, list his or her
name in a note at the top of the first part of your homework.
There should be NO COLLABORATION on exams.
Following "the academic integrity policy", academic misconducts and dishonesty will be reported to the university academic integrity office and seriously affect the grade.
Attendance:
Experience has shown that students who attend class regularly perform better on average. Lectures will involve discussion of topics and usually help students understand the material. Completing the reading assignments is not a substitute for attending lecture, nor is attending lecture a substitute for competing the reading assignments.
Some good references:
Probability and Measure. P. Billingsley, Wiley, 4th edition, 2012.
Elements of Large-Sample Theory. E.L. Lehmann, Springer, 1999.
Theory of Point Estimation. E.L. Lehmann and G. Casella, Springer, 2005.
Testing Statistical Hypothese. E.L. Lehmann and R.P. Romano, Spinger, 3rd edition, 2008.
Mathematical Statistics. P. Bickel and K.A. Doksum, Prentice Hall, 2nd edition, 2006.