Hermite density deconvolution

We consider the additive model: Z = X + ε, where X and ε are independent. We construct a new estimator of the density of X from n observations of Z. We propose a projection method which exploits the specific properties of the Hermite basis. We study the quality of the resulting estimator by proving...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Alea (2006) 2020, Vol.17 (1), p.419-443
1. Verfasser: Sacko, Ousmane
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 443
container_issue 1
container_start_page 419
container_title Alea (2006)
container_volume 17
creator Sacko, Ousmane
description We consider the additive model: Z = X + ε, where X and ε are independent. We construct a new estimator of the density of X from n observations of Z. We propose a projection method which exploits the specific properties of the Hermite basis. We study the quality of the resulting estimator by proving a bound on the integrated quadratic risk. We then propose an adaptive estimation procedure, that is a method of selecting a relevant model. We check that our estimator reaches the classical convergence speeds of deconvolution. Numerical simulations are proposed and a comparison with the results of the method proposed in Comte and Lacour (2011) is performed.
doi_str_mv 10.30757/ALEA.v17-17
format Article
fullrecord <record><control><sourceid>hal_cross</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_01978591v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>oai_HAL_hal_01978591v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c307t-915818e5a27dfc5a7d76cdf56d476fbaf9853a5633bfcc413e5ea485d18be9253</originalsourceid><addsrcrecordid>eNpNkM1Lw0AUxBdRsFZvXgWvgmn3ZfP24xhKNULASz0vm_3ASJrIbgz0vze1Ip5meMzMgx8ht0BXjAoU67LelqsJRAbijCxASZrRgvHzf_6SXKX0QSlXkBcLclf5uG9Hf-98n9rxMKsd-mnovsZ26K_JRTBd8je_uiRvT9vdpsrq1-eXTVlndv47ZgpQgvRocuGCRSOc4NYF5K4QPDQmKInMIGesCdYWwDx6U0h0IBuvcmRL8nDafTed_ozt3sSDHkyrq7LWxxsFJSQqmGDOPp6yNg4pRR_-CkD1DwZ9xKBnDBoE-wZfNU72</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Hermite density deconvolution</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Sacko, Ousmane</creator><creatorcontrib>Sacko, Ousmane</creatorcontrib><description>We consider the additive model: Z = X + ε, where X and ε are independent. We construct a new estimator of the density of X from n observations of Z. We propose a projection method which exploits the specific properties of the Hermite basis. We study the quality of the resulting estimator by proving a bound on the integrated quadratic risk. We then propose an adaptive estimation procedure, that is a method of selecting a relevant model. We check that our estimator reaches the classical convergence speeds of deconvolution. Numerical simulations are proposed and a comparison with the results of the method proposed in Comte and Lacour (2011) is performed.</description><identifier>ISSN: 1980-0436</identifier><identifier>EISSN: 1980-0436</identifier><identifier>DOI: 10.30757/ALEA.v17-17</identifier><language>eng</language><publisher>Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....]</publisher><subject>Mathematics ; Statistics</subject><ispartof>Alea (2006), 2020, Vol.17 (1), p.419-443</ispartof><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c307t-915818e5a27dfc5a7d76cdf56d476fbaf9853a5633bfcc413e5ea485d18be9253</citedby><cites>FETCH-LOGICAL-c307t-915818e5a27dfc5a7d76cdf56d476fbaf9853a5633bfcc413e5ea485d18be9253</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,777,781,882,4010,27904,27905,27906</link.rule.ids><backlink>$$Uhttps://hal.science/hal-01978591$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Sacko, Ousmane</creatorcontrib><title>Hermite density deconvolution</title><title>Alea (2006)</title><description>We consider the additive model: Z = X + ε, where X and ε are independent. We construct a new estimator of the density of X from n observations of Z. We propose a projection method which exploits the specific properties of the Hermite basis. We study the quality of the resulting estimator by proving a bound on the integrated quadratic risk. We then propose an adaptive estimation procedure, that is a method of selecting a relevant model. We check that our estimator reaches the classical convergence speeds of deconvolution. Numerical simulations are proposed and a comparison with the results of the method proposed in Comte and Lacour (2011) is performed.</description><subject>Mathematics</subject><subject>Statistics</subject><issn>1980-0436</issn><issn>1980-0436</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNpNkM1Lw0AUxBdRsFZvXgWvgmn3ZfP24xhKNULASz0vm_3ASJrIbgz0vze1Ip5meMzMgx8ht0BXjAoU67LelqsJRAbijCxASZrRgvHzf_6SXKX0QSlXkBcLclf5uG9Hf-98n9rxMKsd-mnovsZ26K_JRTBd8je_uiRvT9vdpsrq1-eXTVlndv47ZgpQgvRocuGCRSOc4NYF5K4QPDQmKInMIGesCdYWwDx6U0h0IBuvcmRL8nDafTed_ozt3sSDHkyrq7LWxxsFJSQqmGDOPp6yNg4pRR_-CkD1DwZ9xKBnDBoE-wZfNU72</recordid><startdate>2020</startdate><enddate>2020</enddate><creator>Sacko, Ousmane</creator><general>Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....]</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>2020</creationdate><title>Hermite density deconvolution</title><author>Sacko, Ousmane</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c307t-915818e5a27dfc5a7d76cdf56d476fbaf9853a5633bfcc413e5ea485d18be9253</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Mathematics</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sacko, Ousmane</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Alea (2006)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sacko, Ousmane</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hermite density deconvolution</atitle><jtitle>Alea (2006)</jtitle><date>2020</date><risdate>2020</risdate><volume>17</volume><issue>1</issue><spage>419</spage><epage>443</epage><pages>419-443</pages><issn>1980-0436</issn><eissn>1980-0436</eissn><abstract>We consider the additive model: Z = X + ε, where X and ε are independent. We construct a new estimator of the density of X from n observations of Z. We propose a projection method which exploits the specific properties of the Hermite basis. We study the quality of the resulting estimator by proving a bound on the integrated quadratic risk. We then propose an adaptive estimation procedure, that is a method of selecting a relevant model. We check that our estimator reaches the classical convergence speeds of deconvolution. Numerical simulations are proposed and a comparison with the results of the method proposed in Comte and Lacour (2011) is performed.</abstract><pub>Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....]</pub><doi>10.30757/ALEA.v17-17</doi><tpages>25</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1980-0436
ispartof Alea (2006), 2020, Vol.17 (1), p.419-443
issn 1980-0436
1980-0436
language eng
recordid cdi_hal_primary_oai_HAL_hal_01978591v1
source Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals
subjects Mathematics
Statistics
title Hermite density deconvolution
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-19T07%3A36%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Hermite%20density%20deconvolution&rft.jtitle=Alea%20(2006)&rft.au=Sacko,%20Ousmane&rft.date=2020&rft.volume=17&rft.issue=1&rft.spage=419&rft.epage=443&rft.pages=419-443&rft.issn=1980-0436&rft.eissn=1980-0436&rft_id=info:doi/10.30757/ALEA.v17-17&rft_dat=%3Chal_cross%3Eoai_HAL_hal_01978591v1%3C/hal_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true