The correction term in a Small--Ball Probability factorization for random curves

JeanBaptiste Aubin, Enea Giuseppe BONGIORNO, Aldo GOIA

Risultato della ricerca: Contributo su rivistaArticolo in rivistapeer review

Abstract

In this work we propose 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--Lo`{e}ve expansion, a local approach to select the dimensionality is illustrated through numerical and real data examples.
Lingua originaleInglese
RivistaJournal of Multivariate Analysis
Volume189
DOI
Stato di pubblicazionePubblicato - 2022

Keywords

  • Hilbert random elements
  • Karhunen–Loève expansion
  • Nonparametric estimation

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