This course is a continuation of 625.725. Topics covered include principles of data reduction: minimal sufficient, ancillary, and complete statistics, estimation methods: method of moments, maximum likelihood, and Bayesian estimation, Cramer-Rao inequality, uniformly minimum variance unbiased estimators, the Neyman-Pearson lemma, the likelihood ratio test, goodness-of-fit tests, methods of finding confidence intervals: inverting a test statistic, pivotal quantities, pivoting CDF, and Bayesian intervals, asymptotic evaluation of point estimators, asymptotic efficiency of MLE, asymptotic hypothesis testing, and asymptotic confidence intervals including large sample intervals based on MLE. This course is proof oriented.
625.725 Theory of Statistics I or equivalent.
Course all programs:
Applied and Computational Mathematics