Generalized least squares estimation in contingency tables analysis: Asymptotic properties and applications

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.