Minimax optimal estimators for general additive functional estimation

In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very large class of functionals. The optimal minimax rate is shown...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Collier, Olivier, Comminges, Laëtitia
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.08.2019
Subjects
Estimators
Minimax technique
Polynomials
Random noise
Online AccessGet full text

Cover

Abstract In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very large class of functionals. The optimal minimax rate is shown to depend on the polynomial approximation rate of the marginal functional, and optimal estimators achieving this rate are built.
AbstractList In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very large class of functionals. The optimal minimax rate is shown to depend on the polynomial approximation rate of the marginal functional, and optimal estimators achieving this rate are built.
Author Collier, Olivier
Comminges, Laëtitia
Author_xml – sequence: 1
  givenname: Olivier
  surname: Collier
  fullname: Collier, Olivier
– sequence: 2
  givenname: Laëtitia
  surname: Comminges
  fullname: Comminges, Laëtitia
BookMark eNqNi7EKwjAURYMoWLX_EHAupC_WZpeKi5t7KTaRlJpX8xLx840guDodzuXcFZs7dHrGMpCyLNQOYMlyokEIAfsaqkpmrDlbZ-_di-MUEkeu6cOAnrhBz2_aaZ_mru9tsE_NTXTXYNH90iQbtjDdSDr_cs22x-ZyOBWTx0dMXTtg9OlDLYCCWqhSCflf9QZL2z2n
ContentType Paper
Copyright 2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID 8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PIMPY
PQEST
PQQKQ
PQUKI
PRINS
PTHSS
DatabaseName ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central
ProQuest Central Essentials
AUTh Library subscriptions: ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central
SciTech Premium Collection (Proquest) (PQ_SDU_P3)
ProQuest Engineering Collection
Engineering Database
Publicly Available Content Database
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
DatabaseTitle Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest One Academic
Engineering Collection
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2331-8422
Genre Working Paper/Pre-Print
GroupedDBID 8FE
8FG
ABJCF
ABUWG
AFKRA
ALMA_UNASSIGNED_HOLDINGS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FRJ
HCIFZ
L6V
M7S
M~E
PIMPY
PQEST
PQQKQ
PQUKI
PRINS
PTHSS
ID FETCH-proquest_journals_22827081803
IEDL.DBID 8FG
IngestDate Thu Oct 10 16:36:29 EDT 2024
IsOpenAccess true
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-proquest_journals_22827081803
OpenAccessLink https://www.proquest.com/docview/2282708180?pq-origsite=%requestingapplication%
PQID 2282708180
PQPubID 2050157
ParticipantIDs proquest_journals_2282708180
PublicationCentury 2000
PublicationDate 20190829
PublicationDateYYYYMMDD 2019-08-29
PublicationDate_xml – month: 08
  year: 2019
  text: 20190829
  day: 29
PublicationDecade 2010
PublicationPlace Ithaca
PublicationPlace_xml – name: Ithaca
PublicationTitle arXiv.org
PublicationYear 2019
Publisher Cornell University Library, arXiv.org
Publisher_xml – name: Cornell University Library, arXiv.org
SSID ssj0002672553
Score 3.2236898
SecondaryResourceType preprint
Snippet In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More...
SourceID proquest
SourceType Aggregation Database
SubjectTerms Estimators
Minimax technique
Polynomials
Random noise
Title Minimax optimal estimators for general additive functional estimation
URI https://www.proquest.com/docview/2282708180
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LSwMxEB60i-DNJz5qCeg1uCbZ10lo2bUIW4oo9FaSTVYKbl9bwZO_3Uy6qwehx5CQkJDMN_PlYwbgTselUL4oqSxVQUWZcBpro2hQ-DwJWGJCp3bPR-HwTTxPgklDuNWNrLK1ic5Q60WBHPk9s7FBhPnX_MflimLVKPxdbUpo7IP3wKIIg684e_rlWFgYWY-Z_zOzDjuyI_DGcmnWx7Bn5idw4CSXRX0KaT6bzyr5RRb21Vbyg2C-iwpj4JpYT5K8bxNCE1T8oE0iCEFb5q4dahtncJulr4MhbdeeNrejnv7thZ9Dx4b55gKIkYoHWgpeSgQJHVto0ZxjBcsQnZpL6O6a6Wp39zUcWqhPkA1lSRc6m_WnubFwulE9d2Y98PrpaPxiW_l3-gM7m4Dh
link.rule.ids 783,787,12777,21400,33385,33756,43612,43817
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3PS8MwFH7ohujNn_hjakCvwdKkXXPyIKtV1-Fhwm4laRIZ2G2uE_zzzctaPQg7hoSElOR973398h7ArU4sVwG3VFpVUm4Fo4k2ikZlwEQUChN7tXs-irM3_jyJJg3hVjeyytYmekOt5yVy5Hehiw36mH8tuF98UqwahX9XmxIa29DlzGE1vhRPH385ljDuO4-Z_TOzHjvSfei-yoVZHsCWmR3CjpdclvURDPLpbFrJbzJ3t7aSHwTzXVQYA9fEeZLkfZ0QmqDiB20SQQhaM3ftUNc4hpt0MH7IaLt20ZyOuvjbCzuBjgvzzSkQIxWLtOTMSgQJnTho0YxhBcsYnZoz6G2a6Xxz9zXsZuN8WAyfRi8XsOdgXyAzGooedFbLL3PpoHWlrvz3-wFElYD4
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Minimax+optimal+estimators+for+general+additive+functional+estimation&rft.jtitle=arXiv.org&rft.au=Collier%2C+Olivier&rft.au=Comminges%2C+La%C3%ABtitia&rft.date=2019-08-29&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422