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Math5062:
Theory of Statistics II (Spring 2007) |
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Instructor: |
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Office: |
Cupples
I, Room 205 |
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Phone: |
935-5703 |
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Email: |
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Time and location: |
2:00pm
- 3:00pm MWF at Cupples I, Room 216 |
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Office hours: |
By appointment. You are also encouraged to email me your questions. You will receive
my reply within 24 hours with probability 0.95. |
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Textbook: |
Bickel, P. J. and Doksum, K. A. (2001) Mathematical Statistics: Basic Ideas and
Selected Topics (2nd Edition), Prentice Hall. Lehmann, E. L. (2005) Testing Statistical
Hypotheses, 2nd edition, Springer. |
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Prerequisites: |
You should be familiar with the following topics
in probability and mathematical statistics theory. Convergence in
probability; convergence in distribution; law of large numbers; central limit
theorem; slutzky theorem; the delta method; asymptotic normality of the MLE.
If you have questions about the prerequisites, please contact the instructor. |
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Course description: |
This course intends to provide rigorous training
in mathematical statistics for graduate students with sufficient background.
We will focus on the classical mathematical statistics theory of hypothesis
testing, interval estimation and some nonparametric techniques. The topics
include the Neyman-Pearson framework of hypothesis testing, large sample
tests, nonparametric tests, resampling methods and Bayesian methods. |
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Schedule |
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Week 1 |
Introduction,
likelihood-ratio test |
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Week 2 |
Neyman-Pearson
lemma, p-value, UMP tests, Monotone likelihood ratio |
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Week 3 |
Generalized
Neyman-Pearson lemma, UMP tests for two-sided hypotheses, least favorable
distribution |
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Week 4 |
Unbiased
tests, UMPU tests in exponential family |
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Week 5 |
Applications
of the UMPU test theory |
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Week 6 |
More
applications of UMPU test theory, Wald test, score test |
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Week 7 |
Maximum
likelihood ratio test |
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Week 8 |
Theory
of asymptotic tests |
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Week 9 |
Chi-square
tests to categorical data, Bayes tests |
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Week 10 |
Nonparametric
tests, U-statistics, |
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Week 11 |
V-statistics,
Kolmogorov test, |
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Week 12 |
Cramer-von
Mises test |
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Week 13 |
Shapiro-Wilks
tests, |
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Week 14 |
Pivotal
quantity, Inverting acceptance regions of tests, UMA confidence interval, Credible
interval, prediction interval |
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Week 15 |
Bootstrap
method, multiple testing |
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