Exact variable selection in sparse nonparametric models
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11310%2F25%3A10497188" target="_blank" >RIV/00216208:11310/25:10497188 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Z7y4NFV63E" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Z7y4NFV63E</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/25-EJS2374" target="_blank" >10.1214/25-EJS2374</a>
Alternative languages
Result language
angličtina
Original language name
Exact variable selection in sparse nonparametric models
Original language description
We study the problem of adaptive variable selection in a Gaussian white noise model of intensity ε under certain sparsity and regularity conditions on an unknown regression function f. The d-variate regression function f is assumed to be a sum of functions each depending on a smaller number k of variables (1<=k<=d). These functions are unknown to us and only a few of them are nonzero. We assume thatd=d_ε --> infty as ε --> 0 and consider the cases when k is fixed and when k=k_ε --> infty , k=o(d) as ε --> 0. In this work, we introduce an adaptive selection procedure that, under some model assumptions, identifies exactly all nonzero k-variate components of f. In addition, we establish conditions under which exact identification of the nonzero components is impossible. These conditions ensure that the proposed selection procedure is the best possible in the asymptotically minimax sense with respect to the Hamming risk.
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
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Statistics
ISSN
1935-7524
e-ISSN
1935-7524
Volume of the periodical
19
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
32
Pages from-to
2001-2032
UT code for WoS article
001528954600006
EID of the result in the Scopus database
2-s2.0-105003840394