Semiparametric Penalized Spline Regression

TL;DR

This paper introduces a novel semiparametric regression estimator combining parametric and penalized spline methods, with theoretical analysis and practical criteria for model selection, outperforming existing methods.

Contribution

It develops a new semiparametric estimator that integrates parametric and nonparametric penalized spline techniques, along with asymptotic theory and model selection criteria.

Findings

The proposed estimator outperforms kernel-based semiparametric methods.

Numerical experiments confirm the effectiveness of the model selection criteria.

Asymptotic properties depend on both the nonparametric estimator and the parametric residuals.

Abstract

In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the parametric part, while its residual is consistently estimated by the nonparametric part. Asymptotic theory for the proposed semiparametric estimator is developed, showing that its behavior is dependent on the asymptotics for the nonparametric penalized spline estimator as well as on the discrepancy between the true regression function and the parametric part. As a naturally associated application of asymptotics, some criteria for the selection of parametric models are addressed. Numerical experiments show that the proposed estimator performs better than the existing kernel-based semiparametric estimator and the fully nonparametric estimator, and that the proposed criteria work well for choosing a reasonable parametric model.