A. Baccini et al., Generalized least squares estimation in contingency tables analysis: Asymptotic properties and applications, STATISTICS, 34(4), 2000, pp. 267-300
Different sorts of bilinear models (models with bilinear interaction terms)
are currently used when analyzing contingency tables: association models,
correlation models... All these can be included in a general family of bili
near models: power models. In this framework, Maximum Likelihood (ML) estim
ation is not always possible, as explained in an introductory example. Thus
, Generalized Least Squares (GLS) estimation is sometimes needed in order t
o estimate parameters. A subclass of power models is then considered in thi
s paper: separable reduced-rank (SRR) models. They allow an optimal choice
of weights for GLS estimation and simplifications in asymptotic studies con
cerning GLS estimators. Power 2 models belong to the subclass of SRR models
and the asymptotic properties of GLS estimators are established. Similar r
esults are also established for association models which are not SRR models
. However, these results are more difficult to prove. Finally, 2 examples a
re considered to illustrate our results.