On local estimating equations in additive multiparameter models

Estimating all parameters in a multiparameter response model as smooth functions of an explanatory variable is very similar to estimating the different components of an additive model for the response mean. It is shown that, in a general estimating framework, local polynomial backfitting estimators in an additive one-parameter model do not work optimally. For a multiparameter model, however, a backfitting algorithm can be defined that leads to local polynomial estimators that do have optimal properties.