Exercises January 21
STA 4508S (Spring, 2014)
Suppose Yi = (Yi1 , . . . , Yid ) N (0, R), with Rij = 1, if i = j; , if i = j.
1. Show that the pairwise composite log-likelihood function takes the form
c (; y1 , . . . , yn ) =
nm(m 1)
m1+
log(1 2 )
SSw
4
STA 4508: Likelihood and derived quantities
Given a model for Y which assumes Y has a density f (y; ),
the following denitions:
observed likelihood function
log-likelihood function
score function
observed information function
expected information (in one
Edema is the
accumulation of uids in
body tissues.
10.8 - Survival Data 549
computed using only the risk set at time y_,-. A nonconstant plot of observed S_,- against
y,- suggests this type of model failure.
These and other diagnostics for the proportiona
Exercise February 4
STA 4508S (Spring, 2014)
The data set heart in the R library MASS has the Stanford heart-transplant
data, a famous data set from the early 70s, that also appears in the survival
data text by Kalbeisch & Prentice. The treatment variable
Exercise January 28
STA 4508S (Spring, 2014)
SM, Exercise 10.6.4. A model for over-dispersed binomial data can be obtained by assuming that R follows a Binomial(m, p) distribution, and p itself
follows a beta distribution, with density
f (p; , ) =
( + ) 1
Exercises January 7
STA 4508S (Spring, 2014)
1. SM 4.3.3 Plot the likelihood for based on a random sample y1 , . . . , yn
from the density
f (y; ) =
1/(2c) c < y < + c,
0,
otherwise,
where c is a known constant. Find a maximum likelihood estimate of
, and
Exercises January 14
STA 4508S (Spring, 2014)
1. BNC 4.5 Suppose Yij , i = 1, . . . , m; j = 1, . . . , r are independent Bernoulli
random variables with
Pr(Yij = 1) =
ei +j
,
1 + ei +j
where m j = 0. This is known as the Rasch model; in applications
j=1