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P.M.E.ALTHAM, November 1998. Here are some extra problems on generalized linear modelling. These problems are
 

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.
MATHEMATICAL TRIPOS
1994.A1.no11.
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 @`
@fi
and @ 2 `
@fi@fi T .
Show that the matrix @ 2 `

  

Source: Altham, Pat - Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge

 

Collections: Mathematics