Course: MATH 541. Theoretical Statistical Inference (3)
Prerequisites: MATH 340, MATH 450A and MATH 462. Hogg-Craig Theorem, Cochran Theorem, convergence in probability and distribution, Cramer-Wold Theorem, Continuous Mapping Theorem, Weak-Law-of-Large-Numbers, Lindberg-Feller Central Limit Theorem (CLT), Lyapunov CLT, Regular Exponential families, Neyman-Factorization Criterion, the substitution principle, asymptotic relative efficiency, the method of the moments, the MLE and its asymptotic efficiency, Uniformly Minimum Variance Unbiased Estimation, Rao-Blackwell Theorem, Lehmann-Scheffe Theorem, minimal complete sufficient statistics, ancillary statistics, Basu Theorem, confidence regions, likelihood ratio tests, Wilk’s Theorem, Neyman-Pearson Lemma, Uniformly Most Powerful test, Karlin-Rubin Theorem, other large-sample tests.