Topics
Decision theoretic and classical treatments of testing statistical hypotheses including univariate testing in simple and composite cases, exponential families, generalized Neyman-Pearson lemma and application to UMPU single parameter tests, locally best tests, testing in multiparameter Koopman Darmois families, similarity and completeness, application to UMPU tests, including the one and two sample t-tests, group invariance and UMPI tests including the general linear model. Selected topics from sequential testing, optimality of the SPRT, and large sample theory will also be presented.
Grading
Your grade for the course will be determined by your performance on two midterm exams and a final exam. Each will count one third. Problems representative of those on the exams will be assigned during the semester but not collected for grading.
The course is classical in content, but connections to decision-theoretic and Bayesian statistics are established. See course materials.
View course materials and communications.
Some useful elementaryinformation.
Calculate size alpha cutoffs for the standardized test statistic sqrt(n) (barX - mu1)/sigma (sigma known) used for testing the null hypothesis mu1 < mu < mu2 by a UMPU test for iid normal data. Enter particular values in the yellow area, choose "Goal Seek" to set the red cell to zero by adjusting the value, delta, of the gray cell, and read off the cutoffs in the green cells.
We shall follow the course notes most closely, but there is a text, Mathematical Statistics, Vol. 1, second edition, Prentice Hall, 2001, by Peter Bickel and Kjell Doksum. The following references are useful and will be placed on reserve. Some collateral information on invariance is available in the course materials.