STT 871, Theory of Statistics I, Fall 2004
Instructor:
Yijun Zuo
Office: A440 Wells Hall
Tel: 517-432-5413, Email: zuo@msu.edu
Office Hours:
MW 10:00am-11:30am and by appointment
Class Time:
MWF 9:10am-10:00am C101 WH
Textbook:
Mathematical Statistics (by Jun Shao, Springer, 2nd
edition)
Prerequisite:
STT 881 or concurrently (or approval of instructor)
Grading:
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:
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
Dec. 10 Last Day of Classes
Topics:
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)
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