LINEAR MODELS

The general goal of this project is the study of singular linear models is to generalize to singular models results known for models with full rank. The intrinsic property of singular models is that only a subset of the parametric functionals are estimable. A fundamental problem to be considered, when regression models are built, is the presence of nuisance parameters. The nuisance parameters are of minute scientific interest but if they are unnecessarily included there may be loss in efficiency when the main parameters are estimated. On the other hand, if the nuisance parameters are ignored when they are necessary then the estimates of the main parameters may be biased. In the teamwork together with Kenneth Nordström, that started in the late 1980s and resulted in several joint papers (e.g. Fellman and Nordström, 1993, Nordström and Fellman, 1990), the singularity problem and the nuisance parameter problem were combined. Especially, we analysed parametric functionals which are robust both against the presence of nuisance parameters and against the covariance structure of the model (Nordström and Fellman, 1990). In the applied experimental design literature many scientists have showed that although nuisance parameters are ignored some of the main parameters can be estimated without bias. Our contribution is that in addition to these parameters there may be some parametric functionals with the same property. The statistical relevance of these functionals depends on the assumed model. If the model is designed and balanced there may be relevant parameter contrasts which are model-robust. However, if the model is unbalanced then the robust parametric functionals may be of minute statistical relevance (Fellman and Nordström, 1995, 1999).