Optimum Allocation in Linear Regression Theory
If for the estimation of β1, β2different observations (``sources'') of form (1.1) are potentially available, each of them being repeatable as many times as we please, the question arises which of them the experimenter should utilize, and in what proportions. With appropriate optimality con...
Gespeichert in:
| Veröffentlicht in: | The Annals of mathematical statistics 1952-06, Vol.23 (2), p.255-262 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 262 |
|---|---|
| container_issue | 2 |
| container_start_page | 255 |
| container_title | The Annals of mathematical statistics |
| container_volume | 23 |
| creator | Elfving, G. |
| description | If for the estimation of β1, β2different observations (``sources'') of form (1.1) are potentially available, each of them being repeatable as many times as we please, the question arises which of them the experimenter should utilize, and in what proportions. With appropriate optimality conventions the answer is the following. For the estimation of a single quantity of form θ = α1β1+ α2β2the optimum allocation comprises two sources only; for the estimation of both parameters, the corresponding number is two or three; the best proportions are indicated in Sections 2 and 4 below. Generalizations to more than two parameters and to observations at different costs are briefly discussed. The problem is related to Hotelling's weighing problem [2] and to the topics treated by David and Neyman in [1]. |
| doi_str_mv | 10.1214/aoms/1177729442 |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_aoms_1177729442</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>2236451</jstor_id><sourcerecordid>2236451</sourcerecordid><originalsourceid>FETCH-LOGICAL-c357t-a840eeddb95b6cabe55f2d4e92025cc45614a68b0e0d55805626a098fb433a213</originalsourceid><addsrcrecordid>eNptkE1Lw0AURQdRMFbXblzkD6Sd70yWIagVAgVp12EyedEJSSbMpIv-ew0tdePq8i7vnsVB6JngNaGEb7QbwoaQNE1pxjm9QRElUiUqy_AtijDGLOFKkHv0EEK3nEzJCK1302yH4xDnfe-Mnq0bYzvGpR1B-_gTvjyEsJT7b3D-9IjuWt0HeLrkCh3eXvfFNil37x9FXiaGiXROtOIYoGnqTNTS6BqEaGnDIaOYCmO4kIRrqWoMuBFCYSGp1DhTbc0Z05SwFcrP3Mm7DswMR9Pbppq8HbQ_VU7bqjiUl_YSi4DqT8AvY3NmGO9C8NBe5wRXi7J_Fi_nRRdm56_vlDLJBWE_ERtpOg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Optimum Allocation in Linear Regression Theory</title><source>JSTOR Mathematics & Statistics</source><source>JSTOR Archive Collection A-Z Listing</source><source>Project Euclid Open Access</source><source>EZB-FREE-00999 freely available EZB journals</source><source>Project Euclid Complete</source><creator>Elfving, G.</creator><creatorcontrib>Elfving, G.</creatorcontrib><description>If for the estimation of β1, β2different observations (``sources'') of form (1.1) are potentially available, each of them being repeatable as many times as we please, the question arises which of them the experimenter should utilize, and in what proportions. With appropriate optimality conventions the answer is the following. For the estimation of a single quantity of form θ = α1β1+ α2β2the optimum allocation comprises two sources only; for the estimation of both parameters, the corresponding number is two or three; the best proportions are indicated in Sections 2 and 4 below. Generalizations to more than two parameters and to observations at different costs are briefly discussed. The problem is related to Hotelling's weighing problem [2] and to the topics treated by David and Neyman in [1].</description><identifier>ISSN: 0003-4851</identifier><identifier>EISSN: 2168-8990</identifier><identifier>DOI: 10.1214/aoms/1177729442</identifier><language>eng</language><publisher>Institute of Mathematical Statistics</publisher><subject>Coefficients ; Ellipses ; Estimate reliability ; Linear regression ; Mathematical minima ; Minimum value ; Polygons ; Standard deviation ; Statistical variance</subject><ispartof>The Annals of mathematical statistics, 1952-06, Vol.23 (2), p.255-262</ispartof><rights>Copyright 1952 Institute of Mathematical Statistics</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c357t-a840eeddb95b6cabe55f2d4e92025cc45614a68b0e0d55805626a098fb433a213</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2236451$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2236451$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,780,784,803,832,882,885,926,27924,27925,58017,58021,58250,58254</link.rule.ids></links><search><creatorcontrib>Elfving, G.</creatorcontrib><title>Optimum Allocation in Linear Regression Theory</title><title>The Annals of mathematical statistics</title><description>If for the estimation of β1, β2different observations (``sources'') of form (1.1) are potentially available, each of them being repeatable as many times as we please, the question arises which of them the experimenter should utilize, and in what proportions. With appropriate optimality conventions the answer is the following. For the estimation of a single quantity of form θ = α1β1+ α2β2the optimum allocation comprises two sources only; for the estimation of both parameters, the corresponding number is two or three; the best proportions are indicated in Sections 2 and 4 below. Generalizations to more than two parameters and to observations at different costs are briefly discussed. The problem is related to Hotelling's weighing problem [2] and to the topics treated by David and Neyman in [1].</description><subject>Coefficients</subject><subject>Ellipses</subject><subject>Estimate reliability</subject><subject>Linear regression</subject><subject>Mathematical minima</subject><subject>Minimum value</subject><subject>Polygons</subject><subject>Standard deviation</subject><subject>Statistical variance</subject><issn>0003-4851</issn><issn>2168-8990</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1952</creationdate><recordtype>article</recordtype><recordid>eNptkE1Lw0AURQdRMFbXblzkD6Sd70yWIagVAgVp12EyedEJSSbMpIv-ew0tdePq8i7vnsVB6JngNaGEb7QbwoaQNE1pxjm9QRElUiUqy_AtijDGLOFKkHv0EEK3nEzJCK1302yH4xDnfe-Mnq0bYzvGpR1B-_gTvjyEsJT7b3D-9IjuWt0HeLrkCh3eXvfFNil37x9FXiaGiXROtOIYoGnqTNTS6BqEaGnDIaOYCmO4kIRrqWoMuBFCYSGp1DhTbc0Z05SwFcrP3Mm7DswMR9Pbppq8HbQ_VU7bqjiUl_YSi4DqT8AvY3NmGO9C8NBe5wRXi7J_Fi_nRRdm56_vlDLJBWE_ERtpOg</recordid><startdate>19520601</startdate><enddate>19520601</enddate><creator>Elfving, G.</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19520601</creationdate><title>Optimum Allocation in Linear Regression Theory</title><author>Elfving, G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c357t-a840eeddb95b6cabe55f2d4e92025cc45614a68b0e0d55805626a098fb433a213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1952</creationdate><topic>Coefficients</topic><topic>Ellipses</topic><topic>Estimate reliability</topic><topic>Linear regression</topic><topic>Mathematical minima</topic><topic>Minimum value</topic><topic>Polygons</topic><topic>Standard deviation</topic><topic>Statistical variance</topic><toplevel>online_resources</toplevel><creatorcontrib>Elfving, G.</creatorcontrib><collection>CrossRef</collection><jtitle>The Annals of mathematical statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Elfving, G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimum Allocation in Linear Regression Theory</atitle><jtitle>The Annals of mathematical statistics</jtitle><date>1952-06-01</date><risdate>1952</risdate><volume>23</volume><issue>2</issue><spage>255</spage><epage>262</epage><pages>255-262</pages><issn>0003-4851</issn><eissn>2168-8990</eissn><abstract>If for the estimation of β1, β2different observations (``sources'') of form (1.1) are potentially available, each of them being repeatable as many times as we please, the question arises which of them the experimenter should utilize, and in what proportions. With appropriate optimality conventions the answer is the following. For the estimation of a single quantity of form θ = α1β1+ α2β2the optimum allocation comprises two sources only; for the estimation of both parameters, the corresponding number is two or three; the best proportions are indicated in Sections 2 and 4 below. Generalizations to more than two parameters and to observations at different costs are briefly discussed. The problem is related to Hotelling's weighing problem [2] and to the topics treated by David and Neyman in [1].</abstract><pub>Institute of Mathematical Statistics</pub><doi>10.1214/aoms/1177729442</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0003-4851 |
| ispartof | The Annals of mathematical statistics, 1952-06, Vol.23 (2), p.255-262 |
| issn | 0003-4851 2168-8990 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_aoms_1177729442 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Project Euclid Open Access; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | Coefficients Ellipses Estimate reliability Linear regression Mathematical minima Minimum value Polygons Standard deviation Statistical variance |
| title | Optimum Allocation in Linear Regression Theory |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T14%3A13%3A30IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Optimum%20Allocation%20in%20Linear%20Regression%20Theory&rft.jtitle=The%20Annals%20of%20mathematical%20statistics&rft.au=Elfving,%20G.&rft.date=1952-06-01&rft.volume=23&rft.issue=2&rft.spage=255&rft.epage=262&rft.pages=255-262&rft.issn=0003-4851&rft.eissn=2168-8990&rft_id=info:doi/10.1214/aoms/1177729442&rft_dat=%3Cjstor_proje%3E2236451%3C/jstor_proje%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=2236451&rfr_iscdi=true |