Statistics 9720
Mathematical Statistics II
Winter 2007
Instructor
Marco A. R. Ferreira
Office
134

O Middlebush Hall (884

8568)
Email
ferreiram@missouri.edu
Hours
Tuesday and Thursday 2

3pm and by appointment
Text
Ferguson,
A Course in Large Samp
le 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 Inferenc
e
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 A
nalysis 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 need
s 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 specia
l 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.
A
ny 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
expuls
ion. When in doubt about plagiarism, paraphrasing, quoting, or collaboration,
consult the course instructor.
Syllabus
I.
Preliminaries
1.
Overview of Lebesgue integral, absolute continuity, densities
2.
Convergence in probability, laws of large numbers
3.
Con
vergence in distribution
4.
Continuity theorem for characteristic functions (no proof)
5.
Central limit theorems including Lindeberg and Liapunov conditions (no proof)
6.
Cramer

Wold theorem, Multivariate central limit theorem
7.
Transformations and delta method
8.
Order
statistics and asymptotic distribution of quantiles
II.
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.
EM algorithm
2.
Some theory of jackknife and bootstrap
3.
Introduction to generalized linear models, inference
4.
Topics at discretion of instructor
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