Summary: P.M.E.ALTHAM, November 1998.
Here are some extra problems on generalized linear modelling. These problems are
constructed from extracts from recent examination questions for Part IIA of the Cam-
bridge University Mathematics Tripos, which is an examination taken by third-year
mathematics undergraduates, and the Diploma in Mathematical Statistics, which was
an examination taken by rst year graduate students in statistics, now replaced by the
M.Phil. in Statistical Science.
Suppose Y1;:::;Yn are independent observations, with Yi distributed as Poisson with
mean i, where
log( i) = T xi; i = 1;:::;n;
and where x1
T are the rows of a known n p matrix X of rank p. Write down
the log-likelihood `( ) and nd @`
@ and @2`
@ @ T .
Show that the matrix @2`
@ @ T is negative-de nite. How is this relevant to the problem