Shrinking the Quadratic Estimator
We study a regression characterization for the quadratic estimator of weak lensing, developed by Hu and Okamoto (2001,2002), for cosmic microwave background observations. This characterization motivates a modification of the quadratic estimator by an adaptive Wiener filter which uses the robust Baye...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2011-10 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Anderes, Ethan Paul, Debashis |
| description | We study a regression characterization for the quadratic estimator of weak lensing, developed by Hu and Okamoto (2001,2002), for cosmic microwave background observations. This characterization motivates a modification of the quadratic estimator by an adaptive Wiener filter which uses the robust Bayesian techniques described in Strawderman (1971) and Berger (1980). This technique requires the user to propose a fiducial model for the spectral density of the unknown lensing potential but the resulting estimator is developed to be robust to misspecification of this model. The role of the fiducial spectral density is to give the estimator superior statistical performance in a "neighborhood of the fiducial model" while controlling the statistical errors when the fiducial spectral density is drastically wrong. Our estimate also highlights some advantages provided by a Bayesian analysis of the quadratic estimator. |
| doi_str_mv | 10.48550/arxiv.1110.1694 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1110_1694</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2082216440</sourcerecordid><originalsourceid>FETCH-LOGICAL-a510-493e0069f8a1b8b1671cb621b79ffea5e1b3b552bbca128032d53aaf70c1fb9c3</originalsourceid><addsrcrecordid>eNotj81Lw0AUxBdBsNTePUnEc-p7bz-yOUqpH1AQsffwNt21qZrU3UT0vze1ngaGYeY3QlwgzJXVGm44fjdfc8TRQFOqEzEhKTG3iuhMzFLaAQCZgrSWE3H1so1N-9a0r1m_9dnzwJvIfVNny9Q3H9x38VycBn5PfvavU7G-W64XD_nq6f5xcbvKWSPkqpQewJTBMjrr0BRYO0PoijIEz9qjk05rcq5mJAuSNloyhwJqDK6s5VRcHmv_8Kt9HNfjT3W4UR1ujIHrY2Afu8_Bp77adUNsR6SKwBKhUQrkLwXASR0</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2082216440</pqid></control><display><type>article</type><title>Shrinking the Quadratic Estimator</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Anderes, Ethan ; Paul, Debashis</creator><creatorcontrib>Anderes, Ethan ; Paul, Debashis</creatorcontrib><description>We study a regression characterization for the quadratic estimator of weak lensing, developed by Hu and Okamoto (2001,2002), for cosmic microwave background observations. This characterization motivates a modification of the quadratic estimator by an adaptive Wiener filter which uses the robust Bayesian techniques described in Strawderman (1971) and Berger (1980). This technique requires the user to propose a fiducial model for the spectral density of the unknown lensing potential but the resulting estimator is developed to be robust to misspecification of this model. The role of the fiducial spectral density is to give the estimator superior statistical performance in a "neighborhood of the fiducial model" while controlling the statistical errors when the fiducial spectral density is drastically wrong. Our estimate also highlights some advantages provided by a Bayesian analysis of the quadratic estimator.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1110.1694</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Adaptive filters ; Bayesian analysis ; Big Bang theory ; Cosmic microwave background ; Physics - Cosmology and Nongalactic Astrophysics ; Physics - Instrumentation and Methods for Astrophysics ; Regression analysis ; Residential density ; Spectra ; Statistical analysis ; Statistics - Applications ; Wiener filtering</subject><ispartof>arXiv.org, 2011-10</ispartof><rights>2011. 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.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,784,885,27925</link.rule.ids><backlink>$$Uhttps://doi.org/10.48550/arXiv.1110.1694$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.1103/PhysRevD.85.103003$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Anderes, Ethan</creatorcontrib><creatorcontrib>Paul, Debashis</creatorcontrib><title>Shrinking the Quadratic Estimator</title><title>arXiv.org</title><description>We study a regression characterization for the quadratic estimator of weak lensing, developed by Hu and Okamoto (2001,2002), for cosmic microwave background observations. This characterization motivates a modification of the quadratic estimator by an adaptive Wiener filter which uses the robust Bayesian techniques described in Strawderman (1971) and Berger (1980). This technique requires the user to propose a fiducial model for the spectral density of the unknown lensing potential but the resulting estimator is developed to be robust to misspecification of this model. The role of the fiducial spectral density is to give the estimator superior statistical performance in a "neighborhood of the fiducial model" while controlling the statistical errors when the fiducial spectral density is drastically wrong. Our estimate also highlights some advantages provided by a Bayesian analysis of the quadratic estimator.</description><subject>Adaptive filters</subject><subject>Bayesian analysis</subject><subject>Big Bang theory</subject><subject>Cosmic microwave background</subject><subject>Physics - Cosmology and Nongalactic Astrophysics</subject><subject>Physics - Instrumentation and Methods for Astrophysics</subject><subject>Regression analysis</subject><subject>Residential density</subject><subject>Spectra</subject><subject>Statistical analysis</subject><subject>Statistics - Applications</subject><subject>Wiener filtering</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotj81Lw0AUxBdBsNTePUnEc-p7bz-yOUqpH1AQsffwNt21qZrU3UT0vze1ngaGYeY3QlwgzJXVGm44fjdfc8TRQFOqEzEhKTG3iuhMzFLaAQCZgrSWE3H1so1N-9a0r1m_9dnzwJvIfVNny9Q3H9x38VycBn5PfvavU7G-W64XD_nq6f5xcbvKWSPkqpQewJTBMjrr0BRYO0PoijIEz9qjk05rcq5mJAuSNloyhwJqDK6s5VRcHmv_8Kt9HNfjT3W4UR1ujIHrY2Afu8_Bp77adUNsR6SKwBKhUQrkLwXASR0</recordid><startdate>20111008</startdate><enddate>20111008</enddate><creator>Anderes, Ethan</creator><creator>Paul, Debashis</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>EPD</scope><scope>GOX</scope></search><sort><creationdate>20111008</creationdate><title>Shrinking the Quadratic Estimator</title><author>Anderes, Ethan ; Paul, Debashis</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a510-493e0069f8a1b8b1671cb621b79ffea5e1b3b552bbca128032d53aaf70c1fb9c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Adaptive filters</topic><topic>Bayesian analysis</topic><topic>Big Bang theory</topic><topic>Cosmic microwave background</topic><topic>Physics - Cosmology and Nongalactic Astrophysics</topic><topic>Physics - Instrumentation and Methods for Astrophysics</topic><topic>Regression analysis</topic><topic>Residential density</topic><topic>Spectra</topic><topic>Statistical analysis</topic><topic>Statistics - Applications</topic><topic>Wiener filtering</topic><toplevel>online_resources</toplevel><creatorcontrib>Anderes, Ethan</creatorcontrib><creatorcontrib>Paul, Debashis</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Statistics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Anderes, Ethan</au><au>Paul, Debashis</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Shrinking the Quadratic Estimator</atitle><jtitle>arXiv.org</jtitle><date>2011-10-08</date><risdate>2011</risdate><eissn>2331-8422</eissn><abstract>We study a regression characterization for the quadratic estimator of weak lensing, developed by Hu and Okamoto (2001,2002), for cosmic microwave background observations. This characterization motivates a modification of the quadratic estimator by an adaptive Wiener filter which uses the robust Bayesian techniques described in Strawderman (1971) and Berger (1980). This technique requires the user to propose a fiducial model for the spectral density of the unknown lensing potential but the resulting estimator is developed to be robust to misspecification of this model. The role of the fiducial spectral density is to give the estimator superior statistical performance in a "neighborhood of the fiducial model" while controlling the statistical errors when the fiducial spectral density is drastically wrong. Our estimate also highlights some advantages provided by a Bayesian analysis of the quadratic estimator.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1110.1694</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2011-10 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_arxiv_primary_1110_1694 |
| source | arXiv.org; Free E- Journals |
| subjects | Adaptive filters Bayesian analysis Big Bang theory Cosmic microwave background Physics - Cosmology and Nongalactic Astrophysics Physics - Instrumentation and Methods for Astrophysics Regression analysis Residential density Spectra Statistical analysis Statistics - Applications Wiener filtering |
| title | Shrinking the Quadratic Estimator |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-06T00%3A34%3A07IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Shrinking%20the%20Quadratic%20Estimator&rft.jtitle=arXiv.org&rft.au=Anderes,%20Ethan&rft.date=2011-10-08&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1110.1694&rft_dat=%3Cproquest_arxiv%3E2082216440%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2082216440&rft_id=info:pmid/&rfr_iscdi=true |