STAT 713
Mathematical Statistics II

Spring 2003

Location: LeConte 201A
Time: MW 2:30 - 3:45 p.m.

Instructor: W. J. Padgett
E-mail: padgett@stat.sc.edu

Description:

Mathematical Statistics II (3) (Prereq: STAT 712) Further development of estimation theory and tests of hypotheses, including an introduction to Bayes estimation, sufficiency, minimum variance principles, uniformly most powerful and likelihood ratio tests, and sequential probability ratio tests.

Purpose of Course:

To acquaint beginning graduate students in statistics and other disciplines with the concepts of mathematical development of statistical inference. To provide a foundation for further study in statistical theory at both the master's and doctoral levels.

Current Textbook:

A COURSE IN MATHEMATICAL STATISTICS, 2nd Edition, George G. Roussas, Academic Press, 1997.

Topics:

                                                            
   Estimation:  (Sect. 11.1-11.5)                           January 13-22
      Sufficient statistics, completeness, unbiasedness,
      exponential family.
   Estimation:  (Sect. 12.1-12.5, 12.9-12.10)               January 28-February 12
      Method of moments, maximum likelihood principle,
      mean squared error, Cramer-Rao lower bound, best 
      unbiased estimators, consistency, asymptotic
      efficiency.
   EXAM 1                                                   February 17
   Testing Hypotheses:  (Sect. 13.1-13.7)                   February 19-March 24*
      Most powerful tests and the Neyman-Pearson Theorem,
      UMP tests, monotone likelihood ratio, likelihood
      ratio tests, inference for means of normal 
      distributions.
   EXAM 2                                                   March 26
   Confidence Intervals:  (Sect. 15.1-15.4)                 March 31-April 7
      Pivotal quantities, test inversion, confidence 
      regions.
   Sequential Probability Ratio Tests: (Notes** and Ch. 14) April 9-April 16
   Bayesian Methods:  (Sect. 12.6-12.7, 13.9)               April 23-30
      Prior and posterior distributions, loss functions,
      Bayes estimators, Bayesian intervals and tests.

   FINAL EXAM                                               Saturday, May 3, 2:00 pm
                                                           

* Spring Break is March 10-14, 2003.
**Notes on Sequential Analysis will be handed out.

Homework: Homework is an important learning tool. The purpose of homework assignments in this course is to solidify the concepts and help you to understand the results presented and discussed in class. Approximately 8 homework sets will be assigned and turned in for grading. Since each person learns from others, to facilitate working together, you are to do each of the graded homework sets as assigned teams, turning in one paper per team. New teams will be organized after each exam, so each class member will be on three different teams during the semester. Other homework problems will be assigned as "exercises" not to be turned in for grading. Members of the class (chosen randomly, of course) might be asked periodically to write exercise problem solutions on the blackboard for the class.

Attendance and Preparation: All students are expected to attend all classes, be prepared by reading in advance the material to be discussed in class, and to participate in class discussions.

Grading:
The final semester grade will be determined by the weighting:

Tests 1 and 2 - 50%

Homework - 20%

Final Examination - 30%

The overall semester grading scale (percentage) will be:
At least 90% = A; 86-89% = B+; 80-85% = B; 76-79% = C+; 70-75% = C; 66-69% = D+; 60-65% = D; etc.

Some Similar Textbooks:

Introduction to Mathematical Statistics, R.V.Hogg and A.T.Craig

Statistical Inference, G. Casella and R. Berger

Introduction to the Theory of Statistics, A. Mood, F. Graybill and D. Boes

Mathematical Statistics, P. Bickel and K. Doksum

Statistical Theory, B. Lindgren

Office Hours: MW 1:00-2:30 p.m., TTh 10:00-11:30 a.m., or by appointment.

This page ( www.stat.sc.edu/~padgett/courses/stat713/) is maintained by W. J. Padgett (padgett@stat.sc.edu). The views and opinions expressed in this page are strictly those of the page author. The contents of the page have not been reviewed or approved by the University of South Carolina.