Summary: Improving the Precision of Estimation by
fitting a Generalized Linear Model, and
P.M.E.Altham, Statistical Laboratory, University of Cambridge
June 27, 2006
This article was published in the GLIM newsletter No 23, 1994 (ISSN
02690772). It is given on this webpage as I have now added some conjec
tures, and a little numerical example.
Altham (1984) proved a result for maximum likelihood estimators, showing
that one of the purposes of fitting a parsimonious model is to improve the
precision of estimation of those parameters that remain. Here this result is
extended to quasilikelihood and generalized linear models.
2. Statement and Proof of Result
Altham (1984) proved the following result. Suppose that a random sample of
size n has loglikelihood function L n (p), where p is a kdimensional unknown
parameter. Let # be the hypothesis
# : p i = p i (#) for i = 1, · · · , k
where p i (·) are known functions, # is an fdimensional parameter, and f < k.
Suppose that “