Pareto depth for functional data

Sami Helander, Germain Van Bever, Sakke Rantala, Pauliina Ilmonen

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    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.

    Original languageEnglish
    Pages (from-to)182-204
    Number of pages23
    JournalStatistics
    Volume54
    Issue number1
    DOIs
    Publication statusPublished - 2 Jan 2020

    Keywords

    • Functional data analysis
    • Pareto optimality
    • statistical depth

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