The correction term in a small-ball probability factorization for random curves

This work proposes an analysis of the correction term appearing in a Small-Ball Probability factorization for random elements taking values in a separable Hilbert space. Its local nature, its meaning and behavior are discussed also through the derivation of some bounds. Nonparametric kernel-type est...

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Bibliographic Details
Published in:Journal of multivariate analysis 2022-05, Vol.189, p.104891, Article 104891
Main Authors: Aubin, Jean-Baptiste, Bongiorno, Enea G., Goia, Aldo
Format: Article
Language:English
Subjects:
Hilbert random elements
Karhunen–Loève expansion
Nonparametric estimation
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Summary:This work proposes an analysis of the correction term appearing in a Small-Ball Probability factorization for random elements taking values in a separable Hilbert space. Its local nature, its meaning and behavior are discussed also through the derivation of some bounds. Nonparametric kernel-type estimators of the considered statistics are introduced and some asymptotic properties are provided. Finally, in the context of reconstructing a sample of curves by truncated Karhunen–Loève expansion, a local approach to select the dimensionality is illustrated through numerical and real data examples.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2021.104891