Stat 7249: HW 1 solutions
1. a)
The likelihood function of exponential family is
f (y, , ) = exp
y b()
+ c(y, )
a()
Then the generating function can be derived as
y b()
+ c(y, ) dy
a()
y ( + a()t) b( + a()t)
= exp
+ c(y, ) exp
a()
b( + a()t) b()
= exp
a()
HW 1 for Stat 7249 - Spring 2006
Due January 25
Reading in text for this assignment
Chapter 2
Datasets
none for this assignment
1. Cumulants and Cumulant generating function. Let My (t) be the moment generating funtion
for a random variable Y (we will a
HW 2 for Stat 7249 - Spring 2009
Due February 3
Reading in text for this assignment
Chapters 3-5
Datasets
none for this assignment
1. DB Problem 5.1
2. DB Problem 7.1
3. Anscombe residuals are a type of residuals constructed to more closely follow a nor
STA 7249: Generalized Linear Models Assignment 2
1. (Logistic discrimination. Exercise 4.12, McCullagh and Nelder, 1989. See exercise 5.15 for a generalization.) Suppose that a population of individuals is partitioned into two sub-populations or groups, G
STA 7249: Generalized Linear Models Assignment 1
1. This problem concerns the Inverse Gaussian distribution. Let denote the standard normal CDF and consider the function y 0, 0, F (y ) = y y 1 + + e2/ 1 + , y > 0. y y (a) Show that F has density f given b
STA 7249 Sec 0642
Generalized Linear Models
Spring 2006
Instructor: Dr. Mike Daniels (mdaniels@stat.u.edu)
207 Grin-Floyd Hall
392-1941, x235
web page: www.stat.ufl.edu/~mdaniels
Lecture: MWF Period 2, FLO 230
Pre-requisites: STA 6207-6208 and Stat 6327.
STA 7249 Sec 7523
Generalized Linear Models
Spring 2009
Instructor: Dr. Mike Daniels (mdaniels@stat.u.edu)
102C Grin-Floyd Hall
273-1845
web page: www.stat.ufl.edu/~mdaniels
Lecture: T Period 2-3, Th Period 3, FLO 230
Pre-requisites: STA 6207-6208 and Sta
HW 6 for Stat 7249 - Spring 2009
Due April 16
Datasets
none
1. Derive the score test for the conditional likelihood example discussed in class under the case
of mi = 1, i = 1, . . . , n. The resulting test will have a simple closed form.
2. Show that the
HW 5 for Stat 7249 - Spring 2009
Due March 31
Reading in text for this assignment
Chapter 9
Datasets
see below
1. Assume Y P (). Show that Y 1/ N (0, 1) + Op (1/2 ). [Hint: Compute the cumulants
2
of this random variable and examine their behavior relat
HW 4 for Stat 7249 - Spring 2009
Due March 19
Reading in text for this assignment
Chapter 8
Datasets
posted on class web page
1. Show that the complementary log-log model discussed in class (i.e., the Proportional hazards
model) is equivalent to the con
HW 3 for Stat 7249 - Spring 2009
Due February 17
Reading in text for this assignment
Chapter 7
1. Show that the rst four cumulants of Z = Y m , where Y Bin(m, ) are 0, 1, O(m1/2 ),
m (1 )
1
and O(m ), respectively. This implies that for xed , as m , the
HW 3 for Stat 7249 - Spring 2006
Due February 20
Reading in text for this assignment
Chapter 4
Datasets
posted on class web page
1. Show that the rst four cumulants of Z = Y m , where Y Bin(m, ) are 0, 1, O(m1/2 ),
m (1 )
1
and O(m ), respectively. This
HW 1 for Stat 7249 - Spring 2009
Due January 19
Reading in text for this assignment
Chapters 3-5
Datasets
none for this assignment
1. Problem 3.8 in DB
2. Cumulants and Cumulant generating function. Let My (t) be the moment generating funtion
for a rand
STA 7934
Analysis of Longitudinal Data
Fall 2011
Instructor: Dr. Mike Daniels (mdaniels@stat.u.edu)
102C Grin-Floyd
273-1845
web page: www.stat.ufl.edu/~mdaniels
Lecture: T Period 2-3, Th Periods 3, G-F 230
Oce Hours: M,W,Th Period 2 (or call or email)
Co
1
Homework Exercise Set 3: STA 7249
1. (11.23) Consider the model i = , i = 1, . . . , n, assuming v(i ) = i . Suppose actually Var(Yi ) = 2 . Using the univariate version of GEE, show i u() = ^ i (yi -)/ and = y . Show V in V =
i -1 i i i (yi i
[v(i )]-