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

Jean-Baptiste Aubin, Enea G. Bongiorno and Aldo Goia

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

Abstract: 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.

Keywords: Hilbert random elements; Karhunen–Loève expansion; Nonparametric estimation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104891

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