STOR 655 (old Stat 165),   Spring 2008

TTH 11:00-12:15,   Peabody 218

Homepage:   http://www.stat.unc.edu/faculty/cji/655.html

Instructor:   Chuanshu Ji,   Smith 203,   962-3917,   cji@email.unc.edu

Office hours:   make appointment via email

Grader:   Jun Ge

Grade:   Midterm Exam = 20%,   Homework = 30%,   Final Exam = 50%

Exams:

• Midterm Exam:   Thur. 3/6   in class
• Final Exam:   3 hours to be scheduled

  For all exams:   closed-book, calculator needed, tables provided

Text:   ``Statistical Inference (2nd edition)'' by George Casella and Roger Berger, 2001 Duxbury (Thomson Learning)

Homeworks:  

See the assignment list. To help the grader's job and receive credit on your homework, you need to show your work neatly, label each problem clearly, and staple the entire assignment together in the correct order with your name printed on every page. Only some problems will be graded but solutions to all assigned problems will be provided.

Reference books:

• ``Mathematical Statistics (2nd edition, Volume I)'' by Bickel and Doksum, 2001 Prentice Hall
• ``Introduction to Statistical Inference'' by Jack Kiefer, 1987 Springer
• ``Mathematical Statistics'' by Jun Shao, 1999 Springer
• Other books: Schervish, Cox and Hinkley, Rice, Stone, etc.

Course description:   (to be updated and revised as we proceed)

This course is designed for first-year graduate students to learn basic statistical theory and methodology at a ``decent'' mathematical level. It sounds good but can easily end up with a bunch of broken pieces. Too many topics to cover in one semester ... some of them have to be dropped and others need to be highlighted. Here is a tentative plan:
• Cover various parts of the following chapters in two different editions of Casella and Berger --- in the first edition: Chapter 10; in the second edition: Chapters 6 -- 10.
• Stick to basics in both classical statistics and decision theory. Use likelihood (fidelity of model to data) as a thread to link frequentist and Bayesian, parametric and nonparametric, etc.
• Reduce the discussion time spent on certain classical topics, e.g. unbiasedness and invariance, some may be assigned as homeworks.
• Give rigorous arguments to the nice case --- exponential family, and illustrate what can go wrong beyond that via examples.
• Omit linear models (regression and ANOVA) except for some examples.
• Present only ``bare-bones'' in asymptotics without being bogged down by tedious regularity conditions, e.g. the proof of asymptotic normality and efficiency often starts from a Taylor expansion, one way or the other.
• Introduce some modern topics briefly as applications and extensions of the classical theory, e.g. resampling schemes, indirect inference (EM algorithms, Markov chain Monte Carlo) if time permits.