TY - JOUR
T1 - The correction term in a Small--Ball Probability factorization for random curves
AU - Aubin, JeanBaptiste
AU - BONGIORNO, Enea Giuseppe
AU - GOIA, Aldo
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Hilbert random elements
KW - Karhunen–Loève expansion
KW - Nonparametric estimation
KW - Hilbert random elements
KW - Karhunen–Loève expansion
KW - Nonparametric estimation
UR - https://iris.uniupo.it/handle/11579/127068
U2 - 10.1016/j.jmva.2021.104891
DO - 10.1016/j.jmva.2021.104891
M3 - Article
SN - 1095-7243
VL - 189
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -