A Central Limit Theorem for Local Polynomial Backfitting Estimators

Additive models based on backfitting estimators are among the most important recent contributions to modern statistical modelling. However, the statistical properties of backfitting estimators have received relatively little attention. Recently, J.-D. Opsomer and D. Ruppert (1997,Ann. Statist.25, 186-211; 1998,J. Amer. Statist. Assoc.93, 605-619) and J.-D. Opsomer (1997, preprint 96-12, Department of statistics, Iowa State University) derived their mean squared error properties in the case of local polynomial smoothers. In this paper the asymptotic distributional behaviour of backfitting estimators is investigated.