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 thirdyear
mathematics undergraduates, and the Diploma in Mathematical Statistics, which was
an examination taken by first year graduate students in statistics, now replaced by the
M.Phil. in Statistical Science.
Suppose Y 1 ; : : : ; Y n are independent observations, with Y i distributed as Poisson with
mean ¯ i , where
log(¯ i ) = fi T x i ; i = 1; : : : ; n;
and where x 1
T ; : : : ; x n
T are the rows of a known n \Theta p matrix X of rank p. Write down
the loglikelihood `(fi) and find @`
and @ 2 `
@fi@fi T .
Show that the matrix @ 2 `