Pareto depth for functional data. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Helander, Sami; Van Bever, Germain; Rantala, Sakke; Ilmonen, Pauliina
• Is Part Of: Statistics. Volume 54:Issue 1(2020)
• Page Start: 182
• Page End: 204
• Publication Date: 2020-01-02
• Subjects: Functional data analysis -- Pareto optimality -- statistical depth; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2019.1700418
• Languages: English
• ISSNs: 0233-1888

Abstract

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.