703—Introduction to Statistical Theory II. (3) (Prereq: STAT 702) Continuation of STAT 702. Topics include discussion of theoretical properties of point estimators and tests of hypotheses, elements of statistical tests, the Neyman-Pearson Lemma, UMP tests, likelihood ratio and other types of tests, and Bayes procedures in the decision process. Not to be used for M.S. or Ph.D. credit in Statistics.
Sample Course Homepage: Recent Semester
Usually Offered: Even Numbered Springs
Purpose: To expose the student to the basic concepts of theoretical statistics necessary for the solid understanding of the statistical procedures and methods typically used by practicing industrial personnel at an advanced level.
Current Textbook: Mathematical Statistics and Data Analysis (2nd edition), by John A. Rice, Duxbury Press, 1995.
|Sampling and Estimation||
|Properties of Estimators: Sufficiency; consistency; relative efficiency; unbiasedness and MVUE; the Cramer-Rao inequality.||3 weeks|
|Tests of Hypotheses and Their Properties: Elements of a statistical test; significance levels and p-values; power of tests; the Neyman-Pearson theory; UMP tests; specific tests for means, proportions, and variances (one- and two-sample).||4 weeks|
|Other Tests of Hypotheses: Likelihood ratio tests; chi-square and Kolmogorov-Smirnov tests for goodness-of-fit; other basic non-parametric tests for comparing populations||3 weeks|
|Statistical Decision Theory: Loss functions; expected loss; Bayes procedures for estimation and testing, posterior analysis; applications.||1.5 weeks|
The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.