Spring
2009
STAT 7030 – Mathematical Statistics II
|
Date |
Section |
Assignment |
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Jan 13 |
Brief
review of order statistics: maximum and minimum order statistics. Brief review
of estimators. MLE, MOM estimators. Minimum variance estimators. Sufficient
estimators. |
Read
3.10 for order statistics. See class notes on Efficiency and the Cramer-Rao
lower bound, and the class notes on Sufficiency. Read
5.4, 5.5, 5.6. Read Case study 5.4.1: very interesting. Hw#1 (due Jan 20): 5.4.10, 5.4.21,
5.5.3, 5.5.4, 5.5.6, 5.6.3, 5.6.7. |
|
Jan 20 |
Bayesian
estimation (5.8) |
Read
section 5.8 text Read class notes on Bayesian estimation Read the articles A
Bayesian Look at Classical Estimation: The Exponential Distribution (by Abdulaziz Elfessi and David M.
Reineke) and Bayes
Estimators for the Continuous Uniform Distribution by A. Rossman, T Short
and M. Parks Tentative Hw#2 (due Jan 27): 5.8.1, 5.8.3,
5.8.5, 5.8.7. |
|
Jan 27 |
Hypothesis
Testing: testing for means when the population is normal; tests for
proportions. |
Read 6.1-6.3 Read on your own section 6.3
and we will discuss some examples in class. Hw added to Hw#2 (due Feb 3): 6.2.3, 6.2.5, 6.3.3. Think about 6.3.4, 6.3.5, 6.3.7. |
|
Feb 3 |
Type I and type II errors. Power of the test. The Generalized Likelihood Ratio test. (6.4,
6.5) |
Read
sections 6.3-6.5 text. Read 9.1-9.4 class handout. Hw#3 (due Feb. 17): 6.4.5, 6.4.7, 6.4.13 (see example 6.4.2), 6.5.1, 32 (from Rice
handout) Suggested
problems: 6.4.10, 6.4.18, 6.4.19, 6.5.3, 6.5.4, 6.5.5, |
|
Feb 10 |
Distributions
derived from the normal distribution: Chi-square, F and Student
distributions. |
Read 7.1-7.4. Additional problems to Hw#3: 7.3.8, 7.3.9, 7.3.11, 7.3.12. Notice
that I did not assign problems from 7.4 but I believe most of the facts are
known by you. |
|
Feb 17 |
Generating
random data from unusual distributions (see class notes). Robustness of
the t-test. |
Read: 7.4-7.5 and notes (see left). Read from the article How
large does n have to be for Z and t intervals? the first three sections
and be prepared to discuss it in class.
Hw#4 (due Feb. 24): 7.4.24 (see HW4
file for what to do in this problem) 7.5.9, 7.5.14, 7.5.16. I will add to all the questions in section 7.5 that you
should ask yourselves (and also check!) whether the data is coming from a
normal distribution so that you can use the theory presented in sections 7.4
and 7.5. |
|
Feb 24 |
Discuss
the article: How large does n have to be in the Z and t test? |
Hw#5 (due March 3): see file I noticed that I had the first exam scheduled a while
ago and since the Spring break is approaching I will try to bring it to you next
time to have it over the break. |
|
March 3 |
Unfortunately,
no class due to “Little Houdini” |
The
Exam is now posted in |
|
March 10 |
|
No
class Spring break |
|
March 17 |
Tests for two means, two proportions and two variances.
(Chapter 9). Deriving the F-test as a Generalized Likelihood Ratio Test. |
Exam 1 due Read
Chapter 9. Hw#6 (due March 24): 9.2.4, 9.2.11, 9.2.13 (Note: assume
that the sample variance is an unbiased estimator for the variance), 9.3.4,
9.4.4, 9.5.6. Note: On
problems using data plot your data and check the conditions for using the
tests presented in this chapter. |
|
March 24 |
The Multinomial Distribution and the Goodness of Fit
tests. |
Read
10.1 – 10.4. Hw#7 (due March 31): 10.2.2, 10.2.7, 10.2.9, 10.3.2, 10.3.3 (this question
is very interesting), see problem in file, 10.4.3,
10.4.5. |
|
March 31 |
Chi-square test for contingency tables. Tests for
matched pairs (McNemar test). Odds ratio test. |
Read
10.5-10.6. Read class handout: chapter 13. Hw #8 (due April 7): 10.5.4 (see comments on
retrospect studies on handout in regard to odds ratio), 10.5.6 (Can this be seen as a case of McNemar test
for K x K tables? See McNemar test for marginal homogeneity on Resources
page), 10.5.8
(be careful, the “Enrolled” category is out of the “Admitted”). From the class handout: Pb 8, 12 (this looks very interesting) 14,
18. |
|
April 7 |
Covariance and correlation. The Bivariate Normal
distribution. The Linear model. |
Read
11.4, 11.5 Hw #9 (due April 14): 11.4.1, 11.4.2, 11.4.10 (I hope it does not turn out
to be too complicated. The problem is quite intriguing), 11.4.11, 11.5.1 more
to be posted |
|
April 14 |
The Linear Model. |
Read
11.2, 11.3. Hw#10 (due April 21): 11.2.4, 11.2.8, 11.2.16, 11.2.19 (rather than
recalling Question 11.2.14 use pb. 11.2.16 with a*=0), 11.2.21, 11.3.20, 11.3.21. In all
problems involving data please perform the regression analysis yourselves and
do not use the summary provided by the text. Do not
forget to plot the residuals as well to see whether the model is a good fit. |
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April 21 |
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April 28 |
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