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Advances in Data Analysis and Classification

Erschienen in:

19.08.2022 | Regular Article

Localization processes for functional data analysis

verfasst von: Antonio Elías, Raúl Jiménez, J. E. Yukich

Erschienen in: Advances in Data Analysis and Classification | Ausgabe 2/2023

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Abstract

We propose an alternative to k-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies stabilization criteria, we establish pointwise and global approximation results in function spaces when the number of data curves is large. We exploit this feature to develop the asymptotic theory when a finite number of curves is observed at time-points given by an i.i.d. sample whose cardinality increases up to infinity. We use these results to investigate the problem of estimating unobserved segments of a partially observed functional data sample as well as to study the problem of functional classification and outlier detection. For such problems our methods are competitive with and sometimes superior to benchmark predictions in the field. The R package localFDA provides routines for computing the localization processes and the estimators proposed in this article.

Vorheriger Artikel Band depth based initialization of K-means for functional data clustering

Nächster Artikel Nonparametric regression and classification with functional, categorical, and mixed covariates

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Titel: Localization processes for functional data analysis
verfasst von: Antonio Elías
Raúl Jiménez
J. E. Yukich
Publikationsdatum: 19.08.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Advances in Data Analysis and Classification / Ausgabe 2/2023
Print ISSN: 1862-5347
Elektronische ISSN: 1862-5355
DOI: https://doi.org/10.1007/s11634-022-00512-8

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