STAT 608 – Mathematical Statistics II
Spring 2013
Instructor: Anna Liu
Lecture: T, Th 2:30-3:45 LGRT 119
Office: LGRT 1438
Email: anna@math.umass.edu
Web: www.math.umass.edu/~anna/
Homework assignments, solutions, and notes
Office Hours: M 12-1 and W 2:45-3:45 or by appointment
Textbook: Statistical Inference, Second Edition, Casella and Berger (Duxbury)
Reference text: All of Statistics: A concise course in statistical inference, Wasserman, L. (2004).
Description: This is the second part of a two semester sequence on probability and mathematical statistics. ST607 covered probability, basic statistical modelling, and an introduction to the basic methods of statistical inference with application to mainly one sample problem. In ST608 we pick up some additional probability topics as needed and examine further issues in methods of inference including more on likelihood based methods, optimal methods of inference, more large sample methods, Bayesian inference and decision theoretic approaches. The theory is utilized in addressing problems in nonparametric methods, two and multi-sample problems, and categorial, regression and survival models. As with ST607 this is primarily a theory course emphasizing fundamental concepts and techniques. Chapters 6-10 are to be covered.
Stat 607-608 is a sequence of theory courses. Stat 515-516 is also a sequence of calculus based probability and statistics courses but moves at a slower pace. Stat 605 provides a measure-theoretic treatment of probability.
Prerequisites: Stat 607 or permission of instructor
Grading: Homework (35%), Midterm (30%), Final Exam (35%).
Exams: All Exams are in-class and closed book. Calculator is allowed. Make-up exams will only be given for legitimate, documented reasons and when a call has been made to me or the department before the exam.
Midterm (tentative): Thursday, March 7, 2008
Final Exam: will be scheduled later
A rough course schedule:
|
Week |
|
Book Chapters |
Thursday |
|
|---|---|---|---|---|
|
January |
21 |
Sufficiency, Completeness, Exponential family |
6.2, 7.3.3 |
|
|
January |
28 |
Best unbiased estimators |
7.3.2 |
Homework 1 |
|
February |
4 |
Maximum likelihood estimators |
6.3, 7.2.1, 7.2.2 |
Homework 2 |
|
February |
11 |
EM algorithm |
7.2.4 |
Homework 3 |
|
February |
18 |
Bayesian estimators |
7.2.3 |
Homework 4 |
|
February |
25 |
Decision theory |
7.3.1, 7.3.4 |
Homework 5 |
|
March |
4 |
Review and test |
|
|
|
March |
11 |
Hypothesis testing |
8.1, 8.2, 8.3 |
|
|
March |
18 |
Spring break |
||
|
March |
25 |
Confidence intervals |
9.1, 9.2, 9.3 |
Homework 6 |
|
April |
1 |
Asymptotic |
10.1-10.4 |
Homework 7 |
|
April |
8 |
Nonparametric |
supplement materials |
Homework 8 |
|
April |
15 |
Bootstrap |
10.1.4 with supplement materials |
Homework 9 |
|
April |
22 |
Review |
|
Homework 10 |
|
April |
29 |
Exam |
|
|
Homework:
1. Weekly assignments (except when there are exams) are due in class. No late homework is accepted.
2. In writing up homework, it is not sufficient to give only the answer to a problem; you must show how it was calculated (it is not necessary to show detailed calculations, just enough to show that you know what you are doing.).
3. Discussion of homework with fellow students is encouraged, but the final write-up must be your own.