Local additive estimation

TL;DR

The paper introduces a local additive estimator that reduces bias in additive models, maintains stability, and alleviates the curse of dimensionality in high-dimensional nonparametric regression.

Contribution

It proposes a new local additive estimator that localizes additivity assumptions, reducing bias and dimensionality issues while being easy to implement.

Findings

Reduces model bias compared to traditional additive estimators.

Partially alleviates the curse of dimensionality.

Easily implementable with standard additive regression software.

Abstract

Additive models are popular in high--dimensional regression problems because of flexibility in model building and optimality in additive function estimation. Moreover, they do not suffer from the so-called {\it curse of dimensionality} generally arising in nonparametric regression setting. Less known is the model bias incurring from the restriction to the additive class of models. We introduce a new class of estimators that reduces additive model bias and at the same time preserves some stability of the additive estimator. This estimator is shown to partially relieve the dimensionality problem as well. The new estimator is constructed by localizing the assumption of additivity and thus named {\it local additive estimator}. Implementation can be easily made with any standard software for additive regression. For detailed analysis we explicitly use the smooth backfitting estimator by Mammen, Linton and Nielsen (1999).