Adaptive exact recovery in sparse nonparametric models
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00639086" target="_blank" >RIV/67985807:_____/25:00639086 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11203-025-09333-w" target="_blank" >https://doi.org/10.1007/s11203-025-09333-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11203-025-09333-w" target="_blank" >10.1007/s11203-025-09333-w</a>
Alternative languages
Result language
angličtina
Original language name
Adaptive exact recovery in sparse nonparametric models
Original language description
We observe an unknown function of d variables f(t), t ∈ [0, 1]^d, in the Gaussian white noise model of intensity ε > 0. We assume that the function f is regular and that it is a sum of k-variate functions, where k varies from 1 to s (1 ≤ s ≤ d). These functions are unknown to us and only a few of them are nonzero. In this article, we address the problem of identifying the nonzero components of f in the case when d = d_ε → ∞ as ε → 0 and s is either fixed or s = s_ε → ∞, s = o(d) as ε → ∞. This may be viewed as a variable selection problem. We derive the conditions when exact variable selection in the model at hand is possible and provide a selection procedure that achieves this type of selection. The procedure is adaptive to a degree of model sparsity described by the sparsity parameter β ∈ (0, 1). We also derive conditions that make the exact variable selection impossible. Our results augment previous work in this area.
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/EH22_008%2F0004583" target="_blank" >EH22_008/0004583: Research of Excellence on Digital Technologies and Wellbeing</a><br>
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
Statistical Inference for Stochastic Processes
ISSN
1387-0874
e-ISSN
1572-9311
Volume of the periodical
28
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
26
Pages from-to
15
UT code for WoS article
001603299200001
EID of the result in the Scopus database
2-s2.0-105019810440