Ridge reconstruction of partially observed functional data is asymptotically optimal

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114134" target="_blank" >RIV/00216224:14310/20:00114134 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.spl.2020.108813" target="_blank" >https://doi.org/10.1016/j.spl.2020.108813</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.spl.2020.108813" target="_blank" >10.1016/j.spl.2020.108813</a>

Result language
angličtina
Original language name
Ridge reconstruction of partially observed functional data is asymptotically optimal
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GJ17-22950Y" target="_blank" >GJ17-22950Y: Statistical inference for complex stochastic processes in econometric modelling</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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