STATISTICS 613
FALL 2004
Instructor:
Office:
Phone:
Office Hours:
Text:
Dr. T. E. Wehrly
459C Blocker
845-1359
10:30-11:30 MWF, or by appointment.
Shao, Mathematical Statistics , 2nd Edition
• The course grade will be determined according to the following:
Homework 25%
Project 40%
Final Exam (Monday, Dec. 13, 8:00 a.m.) 35%
• Homework will be assigned regularly, and it will be turned in and graded. You may discuss the homework problems with other students, but you should write up your solutions independently. Do not copy other students’ solutions, solutions from previous years, solutions from textbooks or journal articles, or solutions from a solutions manual. Late homework will not be accepted unless you have a university excused absence.
• A grade of Incomplete (I) will be given only in the event that circumstances beyond your control were the cause of your missing class for an extended period. This grade is not to be given because you feel that you have too much other work or study or because you think that you will not earn an acceptable grade in the course.
• ACADEMIC INTEGRITY STATEMENT –”An Aggie does not lie, cheat, or steal or tolerate those who do.” The Aggie Honor Council Rules and Procedures are available at http://www.tamu.edu/aggiehonor.
• STATEMENT ON PLAGIARISM: As commonly defined, plagiarism consists of passing off as one’s own ideas, words, writing, etc., which belong to another. In accordance with this definition, you are committing plagiarism if you copy the work of another person and turn it in as your own, even if you should have the permission of that person. Plagiarism is one of the worst academic sins, for the plagiarist destroys the trust among colleagues without which research cannot be safely communicated.
If you have any questions regarding plagiarism, please consult the latest issue of the
Texas A&M University Student Rules, under the section ”Scholastic Dishonesty.”
• STATEMENT ON DISABILITIES: The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that

all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation for their disabilities. If you believe you have a disability requiring an accommodation, please contact the Office of Support Services for Students with Disabilities in Room 126 of the Koldus Student Services Building. The phone number is 845-1637.
• COPYRIGHT NOTICE: The handouts used in this course are copyrighted. By
“handouts,” I mean all materials generated for this class including syllabi, exams, in-class material, and computer examples. Because these materials are copyrighted, you do not have the right to copy the handouts, unless I expressly grant permission.
• The following books are useful for supplementary reading and additional examples:
Azzalini, Statistical Inference Based on the Likelihood
Barnett, Comparative Statistical Inference
Berger, Statistical Decision Theory
Bickel and Doksum, Mathematical Statistics: Basic Ideas and Selected Topics
Casella and Berger, Statistical Inference
Cox and Hinkley, Theoretical Statistics
Cramer, Mathematical Methods of Statistics
Dobson, Introduction to Generalized Linear Models
Efron and Tibshirani, An Introduction to the Bootstrap
Ferguson, Mathematical Statistics: A Decision Theoretic Approach
Hampel, Ronchetti, Rousseeuw, and Stahel, Robust Statistics: The Approach Based on
Influence Functions
Huber, Robust Statistics
Kiefer, Introduction to Statistical Inference
Lehmann, Elements of Large Sample Theory
Lehmann, Testing Statistical Hypotheses
Lehmann and Casella, Theory of Point Estimation
McCullagh and Nelder, Generalized Linear Models
Pitman, Some Basic Theory of Statistical Inference
Rao, C. R., Linear Statistical Inference and Its Applications
Schervish, Theory of Statistics
Silvey, Statistical Inference
Stuart and Ord, Kendall’s Advanced Theory of Statistics, Vol II, 5th edition
Welsh, Aspects of Statistical Inference
Wilks, Mathematical Statistics
Zacks, The Theory of Statistical Inference

Tentative Syllabus for Statistics 613
1.
Basic concepts — parametric families of distributions, likelihood function, sufficiency, completeness, ancillary statistics, exponential families of distributions, generalized linear models.
2.
Unbiased estimation — review of loss functions and risk functions, mean squared error, UMVUEs, lower bounds for variance, Fisher’s information, efficiency of estimators, bias correction using series expansion or jackknife.
3.
Maximum likelihood estimation — properties of MLEs, computational techniques, EM algorithm, asymptotic distribution, asymptotic efficiency, MLE for GLM, quasi-likelihood.
4.
Decision theoretic estimators — review of Bayesian models, Bayes estimators, minimax estimators, empirical Bayes and shrinkage estimators.
5.
Generalized estimating equations — minimum chi-squared estimators, least squares estimators, general form of estimating equations, M-estimators, asympotic properties of M-estimators, influence functions, robustness.
6.
Variance estimation — substitution method, jackknife, bootstrap estimates of bias and variance.
7.
Basic concepts of hypothesis testing — definitions, MP tests, Neyman-Pearson
Lemma, P -value.
8.
Optimal tests for composite hypotheses — monotone likelihood ratio, UMP tests, similar regions, UMPU tests, tests with Neyman structure, UMPU tests for multiparameter exponential families.
8.
Likelihood ratio tests — likelihood ratio tests, computation of LR statistic, asymptotic properties, related large sample tests including Wald and score tests, Bartlett correction factors, tests for the multinomial distribution, LR tests for GLMs.
9.
Confidence sets — interpretation, pivots, inverting tests, optimal confidence sets, large sample confidence sets, Bayes regions, bootstrap confidence sets.