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Optimal adaptive estimation of linear functionals under sparsity

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1611.09744.pdf (245.3Kb)
Date
2018
Dewey
Analyse
Sujet
Nonasymptotic minimax estimation; adaptive estimation; linear functional; sparsity; unknown noise variance
Journal issue
Annals of Statistics
Volume
46
Number
6
Publication date
2018
Article pages
3130 - 3150
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/17-AOS1653
URI
https://basepub.dauphine.fr/handle/123456789/20881
Collections
  • CEREMADE : Publications
Metadata
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Author
Collier, Olivier
101 Modélisation aléatoire de Paris X [MODAL'X]
Comminges, Laëtitia
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tsybakov, Alexandre
2579 Centre de Recherche en Économie et Statistique [CREST]
Verzelen, Nicolas
1002247 Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie [MISTEA]
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta is an element of R-d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a nonasymptotic rate of convergence that differs from the minimax rate at most by a logarithmic factor. We also show that this optimal adaptive rate cannot be improved when s is unknown. Furthermore, we address the issue of simultaneous adaptation to s and to the variance sigma(2) of the noise. We suggest an estimator that achieves the optimal adaptive rate when both s and sigma(2) are unknown.

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