Fixed-design regression estimation based on real and artificial data

Abstract

In this article, we study the fixed-design regression estimation based on real and artificial data, where the artificial data comes from previously undertaken similar experiments. A least-squares estimate that gives different weights to the real and artificial data is introduced. It is investigated under which condition the rate of convergence of this estimate is better than the rate of convergence of an ordinary least-squares estimate applied to the real data only. The results are illustrated using simulated and real data.

Keywords:

• fixed-design regression
• nonparametric estimation
• L ₂ error
• rate of convergence

AMS Classification:

• Primary: 62G08
• Secondary: 62G20

Acknowledgements

The authors thank the German Research Foundation (DFG) for funding this project within the Collaborative Research Center 666 and the Natural Sciences and Engineering Research Council of Canada for providing additional research support.