A plug-in the number of knots selector for polynomial spline regression

Abstract

A plug-in the number of interior knots (NIKs) selector is proposed for polynomial spline estimation in nonparametric regression. The existence and properties of the optimal NIKs for spline regression are established by minimising the weighted mean integrated squared error. We obtain plug-in formulae for the optimal NIKs based on the theoretical results of asymptotic optimality, and develop strategies for choosing the NIKs of the spline estimator. The proposed NIKs selection method is tested on our simulated data with quite satisfactory performance, and is illustrated by analysing a fossil data set.

Keywords:

• nonparametric regression
• spline
• the number of interior knots
• plug-in
• asymptotic optimality

AMS Subject Classification::

• 62G05
• 62G08
• 62G20

Acknowledgements

The author thanks the editor, an associate editor and two referees for their insightful comments that have helped us to improve this paper.

Funding

This work was supported by the National Science Foundation Award [grant number DMS-1306972].