Functional linear regression with derivatives

Abstract

We introduce a new model of linear regression for random functional inputs taking into account the first-order derivative of the data. We propose an estimation method that comes down to solving a special linear inverse problem. Our procedure tackles the problem through a double and synchronised penalisation. An asymptotic expansion of the mean square prevision error is given. The model and the method are applied to a benchmark dataset of spectrometric curves and compared with other functional models.

Keywords:

• functional data
• linear regression model
• differential operator
• penalisation
• spectrometric curves

AMS Subject Classification :

• 62J99
• 62J07

Acknowledgements

The authors are grateful to the referees and the associate editor for their comments that helped in improving this article.

Notes

Freely downloaded from: http://lib.stat.cmu.edu/datasets/tecator.

Freely downloaded from: http://www.stat.rice.edu marina/codes.html.