Generalized parametric help in Hilbertian additive regression

Abstract

This paper introduces a powerful bias reduction technique applied to local linear additive regression. The main idea is to make use of a parametric family. Existing techniques based on this idea use a parametric model that is linear in the parameter. In this paper we generalize the approaches by allowing nonlinear parametric families. We develop the methodology and theory for response variables taking values in a general separable Hilbert space. Under mild conditions, our proposed approach not only offers flexibility but also gains bias reduction while maintaining the variance of the local linear additive regression estimators. We also provide numerical evidences that support our approach.