STT 872  Theory of Statistics II, Spring 2005

Instructor:
                   Yijun Zuo
                   Office: A440 Wells Hall
                   Tel: 517-432-5413, Email: zuo@msu.edu
Office Hours:
                   MW 11:10am-12:10am  and by appointment
Class Time:
                   MWF 9:10am-10:00am C309 WH
Textbook:
                   Mathematical Statistics (by Jun Shao, Springer)                  

Prerequisite:
                   STT 871; STT 882 or  concurrently (or approval of instructor)
Grading:
                   Exams 80% ( Exam I, 100 points, Final Exam, 100 points) 
                   Homework 20% (about 8 sets of assignments )
                   4.0(>=90%),  3.5(85%-89%), 3.0(80%-84%), 2.5(75%-79%), 2(<=74%)
Assignments:
                   Assignments will be due at the beginning of lecture on the days indicated
                   Late homework is not accepted

Topics:

1. Estimation in parametric models

• Bayes decisions and estimators
• Equivariance
• Minimaxity and Admissibility
• MLE
• Asymptotic efficiency

2. Estimation in nonparametric models

• Distribution estimators
• Statistical Functionals
• Linear Functions of Order Statistics
• Generalized Estimating Equations
• Variance Estimation (Exam I)

3. Hypothesis tests

• UMP tests
• UMP unbiased tests
• UMP invariant tests
• Tests in parametric models
• Tests in nonparametric models

4. Confidence sets

• Construction of confidence sets
• Properties of confidence sets
• Asymptotic confidence sets
• Bootstrap confidence sets
• Simultaneous confidence intervals (Exam II)

References:

1. Lehmann, E.L. (1983). Theory of Point Estimation. John Wiley & Sons

2. Bickel, P.J. and Doksum K.A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics (vol. I). Prentice Hall

3. Rao, C.R. (1973). Linear Statistical Inference and Its Applications. John Wiley & Sons

4. Serfling, R.J. (1980). Approximation Theorems of Mathematical Statistics. John Wiley & Sons

5. Billingsley, P. (1986). Probability and Measures. John Wiley & Sons

The instructor reserves the right to make any changes deemed academically necessary