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Integrated shape-sensitive functional metrics

Author

Listed:
  • Helander, Sami
  • Laketa, Petra
  • Ilmonen, Pauliina
  • Nagy, Stanislav
  • Van Bever, Germain
  • Viitasaari, Lauri

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.

Suggested Citation

  • Helander, Sami & Laketa, Petra & Ilmonen, Pauliina & Nagy, Stanislav & Van Bever, Germain & Viitasaari, Lauri, 2022. "Integrated shape-sensitive functional metrics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21001585
    DOI: 10.1016/j.jmva.2021.104880
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    References listed on IDEAS

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    7. Timmermans, Catherine & Delsol, Laurent & von Sachs, Rainer, 2013. "Using Bagidis in nonparametric functional data analysis: Predicting from curves with sharp local features," LIDAM Reprints ISBA 2013006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Kara, Lydia-Zaitri & Laksaci, Ali & Rachdi, Mustapha & Vieu, Philippe, 2017. "Data-driven kNN estimation in nonparametric functional data analysis," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 176-188.
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