Integrated shape-sensitive functional metrics

Sami Helander, Petra Laketa, Pauliina Ilmonen, Stanislav Nagy, Germain Van Bever and Lauri Viitasaari

Journal of Multivariate Analysis, 2022, vol. 189, issue C

Abstract: This paper develops a new integrated ball (pseudo)metric which provides an intermediary between a chosen starting (pseudo)metric d and the Lp distance in general function spaces. Selecting d as the Hausdorff or Fréchet distances, we introduce integrated shape-sensitive versions of these supremum-based metrics. The new metrics allow for finer analyses in functional settings, not attainable applying the non-integrated versions directly. Moreover, convergent discrete approximations make computations feasible in practice.

Keywords: Fréchet distance; Functional data analysis; Hausdorff distance; Pseudometric (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104880

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