STAT 242b/542b, Yale University, THEORY OF STATISTICS

Yale Main Section: MWF 9:30-10:20am, Becton 102, Prof. Andrew Barron

Yale Pfizer Section: TuTh 4:00-5:30, Groton, Prof. Robb Muirhead

Link for Supplementary Regression Notes: (In Postscript) , (In Pdf format) .

DESCRIPTION: A first course in mathematical statistics. Principles of inference in estimation, hypothesis testing, and regression. ESTIMATION: quantifying the quality of estimators through mean squared error, standard errors, confidence intervals, bootstrap, and calculation or simulation of the sampling distribution. Principles of maximum likelihood, method of moments, and Bayes estimators. Optimal procedures among those which satisfy a particular property, such as unbiasedness, invariance, or asymptotic normality. Efficiency and asymptotic efficiency. HYPOTHESIS TESTS: simple and composite hypotheses concerning distributions and their parameters. Statistical significance. Likelihood ratio, generalized likelihood ratio, and Bayes tests. Cases with most powerful tests. Goodness of fit tests. Tests for location in two or more samples and the analysis of variance. REGRESSION: the method of least squares for one or more explanatory variables. Tests and confidence intervals for coefficients and predictions. Model selection.

PREREQUISITE: Introductory probability (as in STAT 241a/541a). We reinforce these skills with a review (the first week of class) of some of the probability we need in statistics.

TEXT AND HOMEWORK: Most, but not all, of the course material and weekly homework questions are from ``Mathematical Statistics and Data Analysis'' by John Rice, Chapters 8 through 15. Homework counts 30%, class involvement 10%.

EXAMS: Midterm counts 25%, given March 4 (covering Chapters 8,9 and some additional material). Final exam is comprehensive, counts 35%, given May 9. Three pages of notes permitted. Closed book.