Pareto depth for functional data

ABSTRACT

This paper introduces a new concept of depth for functional data. It is based on a new multivariate Pareto depth applied after mapping the functional observations to a vector of statistics of interest. These quantities allow to incorporate the inherent features of the distribution, such as shape or roughness. In particular, in contrast to most existing functional depths, the method is not limited to centrality only. Properties of the depths are explored and the benefits of a flexible choice of features are illustrated on several examples. In particular, its excellent classification capacity is demonstrated on a real data example.

KEYWORDS:

• Functional data analysis
• Pareto optimality
• statistical depth

Acknowledgments

The authors are grateful to two anonymous referees for their careful reading and insightful comments that led to substantial improvements of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The data is shared by Kemijoki Oy to the scientific community for academic research purposes by the original request of Department of Mathematics and Systems Analysis at Aalto University, Finland. Any other use of the data is not allowed. Due to possible competitive advantage reasons, any distinguishing information of the data, including the dates and specific reservoirs, have been removed. The data is not publicly available, but can be redistributed for research purposes on request.