An introductory graduate level course. This is the first part of one-year series course in mathematical statistics.
Instructor: Jimin Ding;
Office: Cupples I, Room 112A;
Email: jmding@math.wustl.edu
TA/Grader: Andrew Womack email: womack.andrew@gmail.com
Office Hours:
Tue. 2:30-4:00pm. and Fri. 3:30-5pm. 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.16 (Thur).
Final: Dec. 16 (Tue) 6-8pm. -- 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:
Homework will be collected every other week on Thursday (starting from Sep. 25th). 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. In class exams have to be finished independently.
Some good references:
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.