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Statistics 9720 Mathematical Statistics II Winter 2007 Instructor Office Email Hours Marco A. R. Ferreira 134-O Middlebush Hall (884-8568) [email protected] Tuesday and Thursday 2-3pm and by appointment Text Ferguson, A Course in Large Sample Theory References Billingsley, Probability and Measure Cramer, Mathematical Methods of Statistics Lehmann, Elements of Large-Sample Theory Lehmann and Casella, Theory of Point Estimation Prakasa Rao, B. L. S., Asymptotic Theory of Statistical Inference Rao, C. R., Linear Statistical Inference and Its Applications, second edition (especially chapters 1-3, 5, 6) Schervish, Theory of Statistics Serfling, Approximation Theorems of Mathematical Statistics Other references Little and Rubin, Statistical Analysis with Missing data McCullogh and Nelder, Generalized Linear Models (Second Edition) Efron and Tibshirani, An Introduction to the Bootstrap Grading Homework (30%), two midterms and final (70%) Students with disabilities: If you have special needs as addressed by the Americans with Disabilities Act (ADA) and need assistance, please notify the Office of Disability Services, A048 Brady Commons, 882-4696 or the course instructor immediately. Reasonable efforts will be made to accommodate your special needs. Honesty: Academic honesty is fundamental to the activities and principles of a university. All members of the academic community must be confident that each person’s work has been responsibly and honorably acquired, developed, and presented. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. The academic community regards academic dishonesty as an extremely serious matter, with serious consequences that range from probation to expulsion. When in doubt about plagiarism, paraphrasing, quoting, or collaboration, consult the course instructor. Syllabus I. Preliminaries 1. 2. 3. 4. 5. 6. 7. 8. II. Overview of Lebesgue integral, absolute continuity, densities Convergence in probability, laws of large numbers Convergence in distribution Continuity theorem for characteristic functions (no proof) Central limit theorems including Lindeberg and Liapunov conditions (no proof) Cramer-Wold theorem, Multivariate central limit theorem Transformations and delta method Order statistics and asymptotic distribution of quantiles Asymptotic methods of inference 1. Asymptotic normality of multinomial vectors, asymptotic distribution of goodness-of-fit chi-square statistic with and without estimated parameters 2. Fisher information and Cramer-Rao lower bound 3. Maximum likelihood theory: consistency and asymptotic normality 4. Method of scoring 5. Asymptotic normality of Bayes posterior mode and posterior distribution. 6. Asymptotic distribution of the likelihood ratio test, Rao’s test and Wald’s test. III. Other topics 1. 2. 3. 4. EM algorithm Some theory of jackknife and bootstrap Introduction to generalized linear models, inference Topics at discretion of instructor