Characterizing Sums of Squares by Their Distributions
In a linear model under normality it is shown that the error sum of squares is characterized by its distribution. Two proofs are presented, one using the almost-sure uniqueness of uniformly minimum variance unbiased estimators and the other using linear algebra. Two illustrations of how this charact...
Gespeichert in:
| Veröffentlicht in: | The American statistician 1997-02, Vol.51 (1), p.55-58 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 58 |
|---|---|
| container_issue | 1 |
| container_start_page | 55 |
| container_title | The American statistician |
| container_volume | 51 |
| creator | Seely, Justus F. Birkes, David Lee, Youngjo |
| description | In a linear model under normality it is shown that the error sum of squares is characterized by its distribution. Two proofs are presented, one using the almost-sure uniqueness of uniformly minimum variance unbiased estimators and the other using linear algebra. Two illustrations of how this characterization can be used are given. |
| doi_str_mv | 10.1080/00031305.1997.10473590 |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_journals_228457234</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>2684696</jstor_id><sourcerecordid>2684696</sourcerecordid><originalsourceid>FETCH-LOGICAL-c339t-3c568cd440ceab6e94d18437823f0227012ae48d78773c3e56b2f9806769e8403</originalsourceid><addsrcrecordid>eNqFkE1LAzEQhoMoWKt_QRb1unXynRylfoLgofUc0jRrU9pNm-wi9de7pa14EU_DDM-8MzwIXWIYYFBwCwAUU-ADrLXsRkxSruEI9TCnsiSS4mPU20LlljpFZznPuxakID3EhzObrGt8Cl-h_ihG7TIXsSpG69Ymn4vJphjPfEjFfchNCpO2CbHO5-iksovsL_a1j94fH8bD5_L17ellePdaOkp1U1LHhXJTxsB5OxFesylWjEpFaAWESMDEeqamUklJHfVcTEilFQgptFcMaB9d7XJXKa5bnxszj22qu5OGEMW4JJR10PVfEJYcVGdBqI4SO8qlmHPylVmlsLRpYzCYrUdz8Gi2Hs3BY7d4s4-32dlFlWztQv7ZJlJpDr-weW5i-h1OKEhDhGJCiw6722GhrmJa2s-YFlPT2M0ipkM0_eejb7Nujow</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>228457234</pqid></control><display><type>article</type><title>Characterizing Sums of Squares by Their Distributions</title><source>Periodicals Index Online</source><source>JSTOR Mathematics & Statistics</source><source>JSTOR Archive Collection A-Z Listing</source><creator>Seely, Justus F. ; Birkes, David ; Lee, Youngjo</creator><creatorcontrib>Seely, Justus F. ; Birkes, David ; Lee, Youngjo</creatorcontrib><description>In a linear model under normality it is shown that the error sum of squares is characterized by its distribution. Two proofs are presented, one using the almost-sure uniqueness of uniformly minimum variance unbiased estimators and the other using linear algebra. Two illustrations of how this characterization can be used are given.</description><identifier>ISSN: 0003-1305</identifier><identifier>EISSN: 1537-2731</identifier><identifier>DOI: 10.1080/00031305.1997.10473590</identifier><identifier>CODEN: ASTAAJ</identifier><language>eng</language><publisher>Alexandria, VA: Taylor & Francis Group</publisher><subject>Algebra ; Chi-squared distribution ; College professors ; Continuous functions ; Covariance matrices ; Degrees of freedom ; Distribution theory ; Error sum of squares ; Exact sciences and technology ; Least squares ; Linear algebra ; Linear hypothesis ; Linear model ; Linear models ; Mathematical analysis ; Mathematical models ; Mathematical theorems ; Mathematical vectors ; Mathematics ; Matrices ; Probability and statistics ; Sciences and techniques of general use ; Statistical inference ; Statistical variance ; Statistics ; Teacher's Corner</subject><ispartof>The American statistician, 1997-02, Vol.51 (1), p.55-58</ispartof><rights>Copyright Taylor & Francis Group, LLC 1997</rights><rights>Copyright 1997 American Statistical Association</rights><rights>1997 INIST-CNRS</rights><rights>Copyright American Statistical Association Feb 1997</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c339t-3c568cd440ceab6e94d18437823f0227012ae48d78773c3e56b2f9806769e8403</citedby><cites>FETCH-LOGICAL-c339t-3c568cd440ceab6e94d18437823f0227012ae48d78773c3e56b2f9806769e8403</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2684696$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2684696$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27869,27924,27925,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2789500$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Seely, Justus F.</creatorcontrib><creatorcontrib>Birkes, David</creatorcontrib><creatorcontrib>Lee, Youngjo</creatorcontrib><title>Characterizing Sums of Squares by Their Distributions</title><title>The American statistician</title><description>In a linear model under normality it is shown that the error sum of squares is characterized by its distribution. Two proofs are presented, one using the almost-sure uniqueness of uniformly minimum variance unbiased estimators and the other using linear algebra. Two illustrations of how this characterization can be used are given.</description><subject>Algebra</subject><subject>Chi-squared distribution</subject><subject>College professors</subject><subject>Continuous functions</subject><subject>Covariance matrices</subject><subject>Degrees of freedom</subject><subject>Distribution theory</subject><subject>Error sum of squares</subject><subject>Exact sciences and technology</subject><subject>Least squares</subject><subject>Linear algebra</subject><subject>Linear hypothesis</subject><subject>Linear model</subject><subject>Linear models</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematical theorems</subject><subject>Mathematical vectors</subject><subject>Mathematics</subject><subject>Matrices</subject><subject>Probability and statistics</subject><subject>Sciences and techniques of general use</subject><subject>Statistical inference</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>Teacher's Corner</subject><issn>0003-1305</issn><issn>1537-2731</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1997</creationdate><recordtype>article</recordtype><sourceid>K30</sourceid><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNqFkE1LAzEQhoMoWKt_QRb1unXynRylfoLgofUc0jRrU9pNm-wi9de7pa14EU_DDM-8MzwIXWIYYFBwCwAUU-ADrLXsRkxSruEI9TCnsiSS4mPU20LlljpFZznPuxakID3EhzObrGt8Cl-h_ihG7TIXsSpG69Ymn4vJphjPfEjFfchNCpO2CbHO5-iksovsL_a1j94fH8bD5_L17ellePdaOkp1U1LHhXJTxsB5OxFesylWjEpFaAWESMDEeqamUklJHfVcTEilFQgptFcMaB9d7XJXKa5bnxszj22qu5OGEMW4JJR10PVfEJYcVGdBqI4SO8qlmHPylVmlsLRpYzCYrUdz8Gi2Hs3BY7d4s4-32dlFlWztQv7ZJlJpDr-weW5i-h1OKEhDhGJCiw6722GhrmJa2s-YFlPT2M0ipkM0_eejb7Nujow</recordid><startdate>19970201</startdate><enddate>19970201</enddate><creator>Seely, Justus F.</creator><creator>Birkes, David</creator><creator>Lee, Youngjo</creator><general>Taylor & Francis Group</general><general>American Statistical Association</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JTYFY</scope><scope>K30</scope><scope>PAAUG</scope><scope>PAWHS</scope><scope>PAWZZ</scope><scope>PAXOH</scope><scope>PBHAV</scope><scope>PBQSW</scope><scope>PBYQZ</scope><scope>PCIWU</scope><scope>PCMID</scope><scope>PCZJX</scope><scope>PDGRG</scope><scope>PDWWI</scope><scope>PETMR</scope><scope>PFVGT</scope><scope>PGXDX</scope><scope>PIHIL</scope><scope>PISVA</scope><scope>PJCTQ</scope><scope>PJTMS</scope><scope>PLCHJ</scope><scope>PMHAD</scope><scope>PNQDJ</scope><scope>POUND</scope><scope>PPLAD</scope><scope>PQAPC</scope><scope>PQCAN</scope><scope>PQCMW</scope><scope>PQEME</scope><scope>PQHKH</scope><scope>PQMID</scope><scope>PQNCT</scope><scope>PQNET</scope><scope>PQSCT</scope><scope>PQSET</scope><scope>PSVJG</scope><scope>PVMQY</scope><scope>PZGFC</scope><scope>0-V</scope><scope>0U~</scope><scope>1-H</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88C</scope><scope>88F</scope><scope>88I</scope><scope>88J</scope><scope>8AF</scope><scope>8C1</scope><scope>8FE</scope><scope>8FG</scope><scope>8FI</scope><scope>8FJ</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ALSLI</scope><scope>AZQEC</scope><scope>BEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>FYUFA</scope><scope>F~G</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>K60</scope><scope>K6~</scope><scope>K9-</scope><scope>L.-</scope><scope>L.0</scope><scope>L6V</scope><scope>M0C</scope><scope>M0R</scope><scope>M0T</scope><scope>M1Q</scope><scope>M2O</scope><scope>M2P</scope><scope>M2R</scope><scope>M7S</scope><scope>MBDVC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0X</scope></search><sort><creationdate>19970201</creationdate><title>Characterizing Sums of Squares by Their Distributions</title><author>Seely, Justus F. ; Birkes, David ; Lee, Youngjo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c339t-3c568cd440ceab6e94d18437823f0227012ae48d78773c3e56b2f9806769e8403</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Algebra</topic><topic>Chi-squared distribution</topic><topic>College professors</topic><topic>Continuous functions</topic><topic>Covariance matrices</topic><topic>Degrees of freedom</topic><topic>Distribution theory</topic><topic>Error sum of squares</topic><topic>Exact sciences and technology</topic><topic>Least squares</topic><topic>Linear algebra</topic><topic>Linear hypothesis</topic><topic>Linear model</topic><topic>Linear models</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematical theorems</topic><topic>Mathematical vectors</topic><topic>Mathematics</topic><topic>Matrices</topic><topic>Probability and statistics</topic><topic>Sciences and techniques of general use</topic><topic>Statistical inference</topic><topic>Statistical variance</topic><topic>Statistics</topic><topic>Teacher's Corner</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Seely, Justus F.</creatorcontrib><creatorcontrib>Birkes, David</creatorcontrib><creatorcontrib>Lee, Youngjo</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Periodicals Index Online Segment 37</collection><collection>Periodicals Index Online</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - West</collection><collection>Primary Sources Access (Plan D) - International</collection><collection>Primary Sources Access & Build (Plan A) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Midwest</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Northeast</collection><collection>Primary Sources Access (Plan D) - Southeast</collection><collection>Primary Sources Access (Plan D) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Southeast</collection><collection>Primary Sources Access (Plan D) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - UK / I</collection><collection>Primary Sources Access (Plan D) - Canada</collection><collection>Primary Sources Access (Plan D) - EMEALA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - International</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - International</collection><collection>Primary Sources Access (Plan D) - West</collection><collection>Periodicals Index Online Segments 1-50</collection><collection>Primary Sources Access (Plan D) - APAC</collection><collection>Primary Sources Access (Plan D) - Midwest</collection><collection>Primary Sources Access (Plan D) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Canada</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - EMEALA</collection><collection>Primary Sources Access & Build (Plan A) - APAC</collection><collection>Primary Sources Access & Build (Plan A) - Canada</collection><collection>Primary Sources Access & Build (Plan A) - West</collection><collection>Primary Sources Access & Build (Plan A) - EMEALA</collection><collection>Primary Sources Access (Plan D) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - Midwest</collection><collection>Primary Sources Access & Build (Plan A) - North Central</collection><collection>Primary Sources Access & Build (Plan A) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - Southeast</collection><collection>Primary Sources Access (Plan D) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - APAC</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - MEA</collection><collection>ProQuest Social Sciences Premium Collection</collection><collection>Global News & ABI/Inform Professional</collection><collection>Trade PRO</collection><collection>ProQuest Central (Corporate)</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Healthcare Administration Database (Alumni)</collection><collection>Military Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Social Science Database (Alumni Edition)</collection><collection>STEM Database</collection><collection>Public Health Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Social Science Premium Collection</collection><collection>ProQuest Central Essentials</collection><collection>eLibrary</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>Health Research Premium Collection</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Consumer Health Database (Alumni Edition)</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ABI/INFORM Professional Standard</collection><collection>ProQuest Engineering Collection</collection><collection>ABI/INFORM Global</collection><collection>Consumer Health Database</collection><collection>Healthcare Administration Database</collection><collection>Military Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Social Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</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>ProQuest Central Basic</collection><collection>SIRS Editorial</collection><jtitle>The American statistician</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Seely, Justus F.</au><au>Birkes, David</au><au>Lee, Youngjo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Characterizing Sums of Squares by Their Distributions</atitle><jtitle>The American statistician</jtitle><date>1997-02-01</date><risdate>1997</risdate><volume>51</volume><issue>1</issue><spage>55</spage><epage>58</epage><pages>55-58</pages><issn>0003-1305</issn><eissn>1537-2731</eissn><coden>ASTAAJ</coden><abstract>In a linear model under normality it is shown that the error sum of squares is characterized by its distribution. Two proofs are presented, one using the almost-sure uniqueness of uniformly minimum variance unbiased estimators and the other using linear algebra. Two illustrations of how this characterization can be used are given.</abstract><cop>Alexandria, VA</cop><pub>Taylor & Francis Group</pub><doi>10.1080/00031305.1997.10473590</doi><tpages>4</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0003-1305 |
| ispartof | The American statistician, 1997-02, Vol.51 (1), p.55-58 |
| issn | 0003-1305 1537-2731 |
| language | eng |
| recordid | cdi_proquest_journals_228457234 |
| source | Periodicals Index Online; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | Algebra Chi-squared distribution College professors Continuous functions Covariance matrices Degrees of freedom Distribution theory Error sum of squares Exact sciences and technology Least squares Linear algebra Linear hypothesis Linear model Linear models Mathematical analysis Mathematical models Mathematical theorems Mathematical vectors Mathematics Matrices Probability and statistics Sciences and techniques of general use Statistical inference Statistical variance Statistics Teacher's Corner |
| title | Characterizing Sums of Squares by Their Distributions |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T06%3A38%3A24IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Characterizing%20Sums%20of%20Squares%20by%20Their%20Distributions&rft.jtitle=The%20American%20statistician&rft.au=Seely,%20Justus%20F.&rft.date=1997-02-01&rft.volume=51&rft.issue=1&rft.spage=55&rft.epage=58&rft.pages=55-58&rft.issn=0003-1305&rft.eissn=1537-2731&rft.coden=ASTAAJ&rft_id=info:doi/10.1080/00031305.1997.10473590&rft_dat=%3Cjstor_proqu%3E2684696%3C/jstor_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=228457234&rft_id=info:pmid/&rft_jstor_id=2684696&rfr_iscdi=true |