STT 871, Theory of Statistics I, Fall 2004  

                   Yijun Zuo
                   Office: A440 Wells Hall
                   Tel: 517-432-5413, Email:
Office Hours:
                   MW 10:00am-11:30am  and by appointment
Class Time:
                   MWF 9:10am-10:00am C101 WH  
                   Mathematical Statistics (by Jun Shao, Springer, 2nd  edition)                  

                   STT 881 or  concurrently (or approval of instructor)
                   Exams 50% ( Exam I, 100 points,  Final Exam, 100 points)       
                   Homework 50% (about 8 sets of assignments )
                   4.0(>=90%),  3.5(85%-89%), 3.0(80%-84%), 2.5(75%-79%), 2.0(<75%)

                   Assignments will be due at the beginning of lecture on the days indicated
                   Late homework is not accepted
Important Dates:

                  Sept. 3 Close of Adds

                  Sept. 6  Labor Day (University Closed)

                  Sept. 23  End of 100% refund

                  Oct. 19 Middle of the semester

                  Nov. 25 & 26 Thanksgiving Holiday (University Closed)

                  Dec. 10 Last Day of Classes


          1. Topics in Probability Theory

1.1     Probability measures, random variables

1.2     Integration and Radon-Nikodym theorem

1.3     Distributions and transformation

1.4     Conditional probability and expectation

1.5     Convergence and limiting distribution                  

              2. Fundamentals of Statistics

2.1     Statistical models

2.2     Sufficiency and completeness

2.3     Estimation and inference

2.4     Decision theory and performance criteria

2.5     Large sample criteria and inference (Middle Exam)

              3. Unbiased estimation

3.1     UMVUE

3.2     U-statistics

3.3     OLSE in linear model

3.4     Unbiased estimators in survey problems

3.5     Asymptotically unbiased estimators

              4. Estimation in parametric models

4.1     Bayes decisions and estimators

4.2     Equivariance

4.3     Minimaxity and Admissibility

4.4     MLE

4.5     Asymptotic efficiency (Final Exam)


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