Local additive estimation

Abstract

Additive models are popular in high dimensional regression problems owing to their
flexibility in model building and optimality in additive function estimation. Moreover, they do not
suffer from the so-called curse of dimensionality generally arising in non-parametric regression
settings. Less known is the model bias that is incurred from the restriction to the additive class of
models.We introduce a new class of estimators that reduces additive model bias, yet preserves
some stability of the additive estimator.The new estimator is constructed by localizing the additivity
assumption and thus is named the local additive estimator. It follows the spirit of local linear
estimation but is shown to be able to relieve partially the dimensionality problem. Implementation
can be easily made with any standard software for additive regression. For detailed analysis we
explicitly use the smooth backfitting estimator of Mammen, Linton and Nielsen.