Estimability in Partitioned Linear Models
Some estimability facts for partitioned linear models with constraints are presented. For a model E(Y) = X1π1+ X2π2with constraints on π1and π2a reduced model is derived that contains all information regarding the estimability (and also regarding the blues) of parametric functions b'π2. For a m...
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| Veröffentlicht in: | The Annals of statistics 1980-03, Vol.8 (2), p.399-406 |
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| container_end_page | 406 |
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| container_issue | 2 |
| container_start_page | 399 |
| container_title | The Annals of statistics |
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| creator | Seely, Justus Birkes, David |
| description | Some estimability facts for partitioned linear models with constraints are presented. For a model E(Y) = X1π1+ X2π2with constraints on π1and π2a reduced model is derived that contains all information regarding the estimability (and also regarding the blues) of parametric functions b'π2. For a model E(Y) = X0π0+ X1π1+ X2π2with constraints on π0, π1and π2, several necessary and sufficient conditions are given for when estimability of b'π2in the original model is equivalent to estimability in the simpler model E(Y) = X0π0+ X2π2. |
| doi_str_mv | 10.1214/aos/1176344960 |
| format | Article |
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For a model E(Y) = X0π0+ X1π1+ X2π2with constraints on π0, π1and π2, several necessary and sufficient conditions are given for when estimability of b'π2in the original model is equivalent to estimability in the simpler model E(Y) = X0π0+ X2π2.</description><identifier>ISSN: 0090-5364</identifier><identifier>EISSN: 2168-8966</identifier><identifier>DOI: 10.1214/aos/1176344960</identifier><language>eng</language><publisher>Institute of Mathematical Statistics</publisher><subject>62J99 ; 62K99 ; Covariance ; Degrees of freedom ; estimable linear parametric functions ; Estimators ; Linear models ; Mathematical vectors ; Matrices ; Parametric models ; Partitioned linear model ; Regression analysis ; Vector space models ; Vector spaces</subject><ispartof>The Annals of statistics, 1980-03, Vol.8 (2), p.399-406</ispartof><rights>Copyright 1980 Institute of Mathematical Statistics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c287t-7e8306e2b60afa9e7819fb27b034f0f1490a13bfb081990b34156f513b7827e33</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2240542$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2240542$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,778,782,801,830,883,924,27907,27908,58000,58004,58233,58237</link.rule.ids></links><search><creatorcontrib>Seely, Justus</creatorcontrib><creatorcontrib>Birkes, David</creatorcontrib><title>Estimability in Partitioned Linear Models</title><title>The Annals of statistics</title><description>Some estimability facts for partitioned linear models with constraints are presented. For a model E(Y) = X1π1+ X2π2with constraints on π1and π2a reduced model is derived that contains all information regarding the estimability (and also regarding the blues) of parametric functions b'π2. For a model E(Y) = X0π0+ X1π1+ X2π2with constraints on π0, π1and π2, several necessary and sufficient conditions are given for when estimability of b'π2in the original model is equivalent to estimability in the simpler model E(Y) = X0π0+ X2π2.</description><subject>62J99</subject><subject>62K99</subject><subject>Covariance</subject><subject>Degrees of freedom</subject><subject>estimable linear parametric functions</subject><subject>Estimators</subject><subject>Linear models</subject><subject>Mathematical vectors</subject><subject>Matrices</subject><subject>Parametric models</subject><subject>Partitioned linear model</subject><subject>Regression analysis</subject><subject>Vector space models</subject><subject>Vector spaces</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1980</creationdate><recordtype>article</recordtype><recordid>eNplkL1PwzAQxS0EEqGwMjFkZUh7_ogdb6CofEhBMNA5shNbchTiyjZD_3uCGpWB6Unv7vd07xC6xbDGBLON8nGDseCUMcnhDGUE86qoJOfnKAOQUJSUs0t0FeMAAKVkNEP325jcl9JudOmQuyn_UCG55Pxk-rxxk1Ehf_O9GeM1urBqjOZm0RXaPW0_65eieX9-rR-boiOVSIUwFQVuiOagrJJGVFhaTYQGyixYzCQoTLXVMA8kaMpwyW05W6IiwlC6Qg_H3H3wg-mS-e5G17f7MJ8ZDq1Xrq13zeIuMldv_6rPEetjRBd8jMHYE42h_f3Vf-DuCAwx-XDaJoRByQj9AbGoZV8</recordid><startdate>19800301</startdate><enddate>19800301</enddate><creator>Seely, Justus</creator><creator>Birkes, David</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19800301</creationdate><title>Estimability in Partitioned Linear Models</title><author>Seely, Justus ; Birkes, David</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c287t-7e8306e2b60afa9e7819fb27b034f0f1490a13bfb081990b34156f513b7827e33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1980</creationdate><topic>62J99</topic><topic>62K99</topic><topic>Covariance</topic><topic>Degrees of freedom</topic><topic>estimable linear parametric functions</topic><topic>Estimators</topic><topic>Linear models</topic><topic>Mathematical vectors</topic><topic>Matrices</topic><topic>Parametric models</topic><topic>Partitioned linear model</topic><topic>Regression analysis</topic><topic>Vector space models</topic><topic>Vector spaces</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Seely, Justus</creatorcontrib><creatorcontrib>Birkes, David</creatorcontrib><collection>CrossRef</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Seely, Justus</au><au>Birkes, David</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Estimability in Partitioned Linear Models</atitle><jtitle>The Annals of statistics</jtitle><date>1980-03-01</date><risdate>1980</risdate><volume>8</volume><issue>2</issue><spage>399</spage><epage>406</epage><pages>399-406</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><abstract>Some estimability facts for partitioned linear models with constraints are presented. For a model E(Y) = X1π1+ X2π2with constraints on π1and π2a reduced model is derived that contains all information regarding the estimability (and also regarding the blues) of parametric functions b'π2. For a model E(Y) = X0π0+ X1π1+ X2π2with constraints on π0, π1and π2, several necessary and sufficient conditions are given for when estimability of b'π2in the original model is equivalent to estimability in the simpler model E(Y) = X0π0+ X2π2.</abstract><pub>Institute of Mathematical Statistics</pub><doi>10.1214/aos/1176344960</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | The Annals of statistics, 1980-03, Vol.8 (2), p.399-406 |
| issn | 0090-5364 2168-8966 |
| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; Jstor Complete Legacy; Project Euclid Complete |
| subjects | 62J99 62K99 Covariance Degrees of freedom estimable linear parametric functions Estimators Linear models Mathematical vectors Matrices Parametric models Partitioned linear model Regression analysis Vector space models Vector spaces |
| title | Estimability in Partitioned Linear Models |
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