Semi-parametric regression: Efficiency gains from modeling the nonparametric part

TL;DR

This paper demonstrates that imposing structure on the nonparametric component of semi-parametric models, such as additivity, can significantly improve the efficiency of estimating the parametric part, with theoretical bounds and practical estimators.

Contribution

It derives the semi-parametric Fisher information bound for additive models and proposes efficient estimators using smooth backfitting, illustrating efficiency gains in semi-parametric estimation.

Findings

Efficiency gains from structured nonparametric modeling.

Semi-parametric Fisher information bound derived.

Proposed estimators perform well in finite samples.

Abstract

It is widely admitted that structured nonparametric modeling that circumvents the curse of dimensionality is important in nonparametric estimation. In this paper we show that the same holds for semi-parametric estimation. We argue that estimation of the parametric component of a semi-parametric model can be improved essentially when more structure is put into the nonparametric part of the model. We illustrate this for the partially linear model, and investigate efficiency gains when the nonparametric part of the model has an additive structure. We present the semi-parametric Fisher information bound for estimating the parametric part of the partially linear additive model and provide semi-parametric efficient estimators for which we use a smooth backfitting technique to deal with the additive nonparametric part. We also present the finite sample performances of the proposed estimators and analyze Boston housing data as an illustration.