A Simple Smooth Backfitting Method for Additive Models

In this paper a new smooth backfitting estimate is proposed for additive regression models. The estimate has the simple structure of Nadaraya–Watson smooth backfitting but at the same time achieves the oracle property of local linear smooth backfitting. Each component is estimated with the same asymptotic accuracy as if the other components were known. 1. Introduction. In additive models it is assumed that the influence of different covariates enters separately into the regression model and that the regression function can be modeled as the sum of the single influences. This is often a plausible assumption. It circumvents fitting of high-dimensional curves and for this reason it avoids the so-called curse of dimensionality. On the other hand, it is a very flexible model that also allows good approximations for more complex structures. Furthermore, the low-dimensional curves fitted in the additive model can be easily visualized in plots. This allows a good data-analytic interpretation of the qualitative influence of single co-variates. In this paper we propose a new backfitting estimate for additive regression models. The estimate is a modification of the smooth backfitting estimate of Mammen, Linton and Nielsen [9]. Their versions of smooth backfitting have been introduced for Nadaraya–Watson smoothing and for local linear smoothing. Smooth backfitting based on Nadaraya–Watson smoothing has the advantage of being easily implemented and of having rather simple intuitive interpretations. On the other hand, local linear smooth backfitting