Classification Using Censored Functional Data

Abstract

We consider classification of functional data when the training curves are not observed on the same interval. Different types of classifier are suggested, one of which involves a new curve extension procedure. Our approach enables us to exploit the information contained in the endpoints of these intervals by incorporating it in an explicit but flexible way. We study asymptotic properties of our classifiers, and show that, in a variety of settings, they can even produce asymptotically perfect classification. The performance of our techniques is illustrated in applications to real and simulated data. Supplementary materials for this article are available online.

KEY WORDS:

• Bagging
• Cross-validation
• Functional principal components
• Incomplete curves
• Perfect classification
• Quadratic discriminant

Acknowledgments

This research was supported by grants and fellowships from the Australian Research Council. The authors thank the editor, the associate editor, and two referees for their valuable comments that helped improve a previous version of the article.