Statistics 659
1 Chapter 1Introduction
Categorical data
Response and explanatory variables
Nominal and ordinal data
Models for categorical data
1. Binomial distribution
2. Poisson distribution
3. Multinomial distribution
Inference for the binomial pr

Statistics 643
Homework #9
Due Friday, April 26, 2013
1. Consider the situation of Problem 3 of Homework #4 and Problem 1 of Homework #8. Below are
some data artificially generated from an exponential distribution:
0.24, 3.20, 0.14, 1.86, 0.58, 1.15, 0.32

Statistics 643
Homework #7
Due Friday, April 12, 2013
1. (Shao Exercise 2.64) Let X1 , . . . , Xn be iid binary random variables with P (Xi = 1) = (0, 1)
and P (Xi = 0) = 1 , for i = 1, . . . , n. Consider estimating with the squared error loss. Let
X = (

Statistics 643
Homework #3
Due Friday, February 8, 2013
1. Prove Theorem 32 from the class notes. [Parts 1), 2), and 5) are optional.]
2. (Cressie) Let = [, ] for some > 0, F be the set of Borel sets, and P be the Lebesgue measure
divided by 2. For a subs

Statistics 643
Homework #2
Due Friday, February 1, 2013
Note: For each of the questions 4, 5, and 9, if you give a correct example that is significantly different from
the examples provided by your classmates, you will receive additional bonus points that

Statistics 643
Homework #1
Due Friday, January 25, 2013
1. (Some simple facts about complex analysis)
(a) Find the series expansions of exp(x), cos(x), and sin(x) for real numbers x. Substitute the
imaginary number i (for real) into the expansion of exp(x

Statistics 643
Homework #8
Due Friday, April 19, 2013
1. Consider the situation of Problem 3 of Homework #4 and the maximum likelihood estimation of
based on X1 , . .P
. , Xn , which are iid with the distribution PX . Let i = I[Xi 6= 0], for i = 1, . . .

Statistics 643
Homework #10
Self-Practice
1. Suppose that the conditions of Theorem 197 (the Cramer-Rao inequality) hold for all . Let h
0
0
be a function from to R1 such that h is continuous and h () 6= 0 for all . Let = h() and
define Q = P . Show that

Statistics 643
Homework #4
Due Friday, February 22, 2013
1. Prove the R1 (i.e., k = 1) version of Lehmanns Theorem (Lemma 51 from the class notes). (Hint:
Consider first indicator functions for , and then simple functions, non-negative functions, and gene

Statistics 643
Homework #5
Due Friday, March 1, 2013
1. Let P0 and P1 be two distributions on X and f0 and f1 be their densities with respect to a dominating
-finite measure . Consider the parametric family of distributions with parameter [0, 1]
and densi

Statistics 643
Homework #6
Due Friday, March 29, 2013
1. Let X be a discrete (measurable) random observable and T (X) be a statistic. Prove the following
theorem, the discrete X version of Theorem 89:
IX (P, Q) IT (X) (P T , QT ), and there is equality if