Download Statistics 9720 Mathematical Statistics II Winter 2007

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