Convergence in probability, in distribution, in mean. Review of the central limit theorem and the weak law of large numbers. Point estimation. Method of moments. Maximum likelihood. Fisher information. Information bound. Properties of maximum likelihood estimation. Newton Raphson and EM algorithms. Sufficiency. Exponential families. Blackwell Rao Theorem. The bootstrap method. Confidence intervals. Hypothesis Testing. Errors. Optimality for tests. Neyman–Pearson tests and optimal tests for one-sided hypotheses. Generalized likelihood ratio tests. Elements of Bayesian estimation and decision theory. Prerequisites: STAT 233, or STAT 230 with consent of instructor. Annually.

Statistical Inference