Scalar-on-function local linear regression and beyond
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452435" target="_blank" >RIV/00216208:11320/22:10452435 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=M1ECjJTfNt" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=M1ECjJTfNt</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/biomet/asab027" target="_blank" >10.1093/biomet/asab027</a>
Alternative languages
Result language
angličtina
Original language name
Scalar-on-function local linear regression and beyond
Original language description
It is common to want to regress a scalar response on a random function. This paper presents results that advocate local linear regression based on a projection as a nonparametric approach to this problem. Our asymptotic results demonstrate that functional local linear regression outperforms its functional local constant counterpart. Beyond the estimation of the regression operator itself, local linear regression is also a useful tool for predicting the functional derivative of the regression operator, a promising mathematical object in its own right. The local linear estimator of the functional derivative is shown to be consistent. For both the estimator of the regression functional and the estimator of its derivative, theoretical properties are detailed. On simulated datasets we illustrate good finite-sample properties of the proposed methods. On a real data example of a single-functional index model, we indicate how the functional derivative of the regression operator provides an original, fast and widely applicable estimation method.
Czech name
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Czech description
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Classification
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
Result continuities
Project
<a href="/en/project/GJ19-16097Y" target="_blank" >GJ19-16097Y: Geometric aspects of mathematical statistics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Biometrika
ISSN
0006-3444
e-ISSN
1464-3510
Volume of the periodical
109
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
17
Pages from-to
439-455
UT code for WoS article
000769813800001
EID of the result in the Scopus database
2-s2.0-85132115681