Theoretical Statistics I

Prerequisites: students in a masters program must seek the director of the M.A. program in statistics' permission; students in an undergraduate program must seek the director of undergraduate studies in statistics' permission. A general introduction to mathematical statistics and statistical decision theory. Elementary decision theory, Bayes inference, Neyman-Pearson theory, hypothesis testing, most powerful unbiased tests, confidence sets. Estimation: methods, theory, and asymptotic properties. Likelihood ratio tests, multivariate distribution. Elements of general linear hypothesis, invariance, nonparametric methods, sequential analysis.