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@article{1655218,
author = {Kraus, David and Stefanucci, Marco},
article_location = {Amsterdam},
article_number = {OCT 2020},
doi = {http://dx.doi.org/10.1016/j.spl.2020.108813},
keywords = {Functional data; Partial observation; Reconstruction; Reproducing kernel Hilbert space; Ridge regularization},
language = {eng},
issn = {0167-7152},
journal = {Statistics and Probability Letters},
title = {Ridge reconstruction of partially observed functional data is asymptotically optimal},
url = {https://doi.org/10.1016/j.spl.2020.108813},
volume = {165},
year = {2020}
}
TY - JOUR
ID - 1655218
AU - Kraus, David - Stefanucci, Marco
PY - 2020
TI - Ridge reconstruction of partially observed functional data is asymptotically optimal
JF - Statistics and Probability Letters
VL - 165
IS - OCT 2020
SP - 1-5
EP - 1-5
PB - Elsevier
SN - 01677152
KW - Functional data
KW - Partial observation
KW - Reconstruction
KW - Reproducing kernel Hilbert space
KW - Ridge regularization
UR - https://doi.org/10.1016/j.spl.2020.108813
L2 - https://doi.org/10.1016/j.spl.2020.108813
N2 - When functional data are observed on parts of the domain, it is of interest to recover the missing parts of curves. Kraus (2015) proposed a linear reconstruction method based on ridge regularization. Kneip and Liebl (2019) argue that an assumption under which Kraus (2015) established the consistency of the ridge method is too restrictive and propose a principal component reconstruction method that they prove to be asymptotically optimal. In this note we relax the restrictive assumption that the true best linear reconstruction operator is Hilbert–Schmidt and prove that the ridge method achieves asymptotic optimality under essentially no assumptions. The result is illustrated in a simulation study.
ER -
KRAUS, David and Marco STEFANUCCI. Ridge reconstruction of partially observed functional data is asymptotically optimal. \textit{Statistics and Probability Letters}. Amsterdam: Elsevier, 2020, vol.~165, OCT 2020, p.~1-5. ISSN~0167-7152. Available from: https://dx.doi.org/10.1016/j.spl.2020.108813.
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