Summary: Improving the Precision of Estimation by
fitting a Generalized Linear Model, and
Quasi­likelihood.
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.
1. Introduction
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 “

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

Collections: Mathematics