Nonconcave Penalized Spline

TL;DR

This paper introduces a non-concave penalized regression spline method that adaptively selects optimal knots and achieves optimal convergence, improving nonparametric regression flexibility and performance.

Contribution

It proposes a novel non-concave penalized spline approach that automatically determines knot placement and handles smoothing parameter selection.

Findings

Method achieves optimal convergence rate.

Performance superior in simulations compared to existing methods.

Insensitive to initial number of knots.

Abstract

Regression spline is a useful tool in nonparametric regression. However, finding the optimal knot locations is a known difficult problem. In this article, we introduce the Non-concave Penalized Regression Spline. This proposal method not only produces smoothing spline with optimal convergence rate, but also can adaptively select optimal knots simultaneously. It is insensitive to the number of origin knots. The method's performance in a simulation has been studied to compare the other methods. The problem of how to choose smoothing parameters, i.e. penalty parameters in the non-concave regression spline is addressed.