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A New Estimator of the Variance Based on Minimizing Mean Squared Error
In 2005, Yatracos constructed the estimator S 2 2 = c 2 S 2 , c 2 = (n + 2)(n − 1)[n(n + 1)] − 1 , of the variance, which has smaller mean squared error (MSE) than the unbiased estimator S 2 . In this work, the estimator S 2 1 = c 1 S 2 , c 1 = n(n − 1)[n(n − 1) + 2] − 1 , is constructed and is show...
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| Published in: | The American statistician 2012-11, Vol.66 (4), p.234-236 |
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| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c357t-788d29faeeca957ca6e818079e8e9932aac17bffe21014f97b8c00bc4fab87393 |
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| cites | cdi_FETCH-LOGICAL-c357t-788d29faeeca957ca6e818079e8e9932aac17bffe21014f97b8c00bc4fab87393 |
| container_end_page | 236 |
| container_issue | 4 |
| container_start_page | 234 |
| container_title | The American statistician |
| container_volume | 66 |
| creator | Kourouklis, Stavros |
| description | In 2005, Yatracos constructed the estimator S
2
2
= c
2
S
2
, c
2
= (n + 2)(n − 1)[n(n + 1)]
− 1
, of the variance, which has smaller mean squared error (MSE) than the unbiased estimator S
2
. In this work, the estimator S
2
1
= c
1
S
2
, c
1
= n(n − 1)[n(n − 1) + 2]
− 1
, is constructed and is shown to have the following properties: (a) it has smaller MSE than S
2
2
, and (b) it cannot be improved in terms of MSE by an estimator of the form cS
2
, c > 0. The method of construction is based on Stein's classical idea brought forward in 1964, is very simple, and may be taught even in an undergraduate class. Also, all the estimators of the form cS
2
, c > 0, with smaller MSE than S
2
as well as all those that have the property (b) are found. In contrast to S
2
, the method of moments estimator is among the latter estimators. |
| doi_str_mv | 10.1080/00031305.2012.735209 |
| format | article |
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2
2
= c
2
S
2
, c
2
= (n + 2)(n − 1)[n(n + 1)]
− 1
, of the variance, which has smaller mean squared error (MSE) than the unbiased estimator S
2
. In this work, the estimator S
2
1
= c
1
S
2
, c
1
= n(n − 1)[n(n − 1) + 2]
− 1
, is constructed and is shown to have the following properties: (a) it has smaller MSE than S
2
2
, and (b) it cannot be improved in terms of MSE by an estimator of the form cS
2
, c > 0. The method of construction is based on Stein's classical idea brought forward in 1964, is very simple, and may be taught even in an undergraduate class. Also, all the estimators of the form cS
2
, c > 0, with smaller MSE than S
2
as well as all those that have the property (b) are found. In contrast to S
2
, the method of moments estimator is among the latter estimators.</description><identifier>ISSN: 0003-1305</identifier><identifier>EISSN: 1537-2731</identifier><identifier>DOI: 10.1080/00031305.2012.735209</identifier><identifier>CODEN: ASTAAJ</identifier><language>eng</language><publisher>Alexandria: Taylor & Francis Group</publisher><subject>Admissibility ; Bayes estimators ; Error rates ; Estimates ; Estimation methods ; Estimators ; Estimators for the mean ; Higher education ; Mathematical constants ; Mean square errors ; Method of moments ; Population estimates ; Statistical variance ; Statistics ; Stein's method ; Teacher's Corner ; Unbiased estimators ; Variance estimation</subject><ispartof>The American statistician, 2012-11, Vol.66 (4), p.234-236</ispartof><rights>Copyright Taylor & Francis Group, LLC 2012</rights><rights>Copyright 2012 American Statistical Association</rights><rights>Copyright Taylor & Francis Ltd. 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c357t-788d29faeeca957ca6e818079e8e9932aac17bffe21014f97b8c00bc4fab87393</citedby><cites>FETCH-LOGICAL-c357t-788d29faeeca957ca6e818079e8e9932aac17bffe21014f97b8c00bc4fab87393</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/23339501$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/23339501$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,58238,58471</link.rule.ids></links><search><creatorcontrib>Kourouklis, Stavros</creatorcontrib><title>A New Estimator of the Variance Based on Minimizing Mean Squared Error</title><title>The American statistician</title><description>In 2005, Yatracos constructed the estimator S
2
2
= c
2
S
2
, c
2
= (n + 2)(n − 1)[n(n + 1)]
− 1
, of the variance, which has smaller mean squared error (MSE) than the unbiased estimator S
2
. In this work, the estimator S
2
1
= c
1
S
2
, c
1
= n(n − 1)[n(n − 1) + 2]
− 1
, is constructed and is shown to have the following properties: (a) it has smaller MSE than S
2
2
, and (b) it cannot be improved in terms of MSE by an estimator of the form cS
2
, c > 0. The method of construction is based on Stein's classical idea brought forward in 1964, is very simple, and may be taught even in an undergraduate class. Also, all the estimators of the form cS
2
, c > 0, with smaller MSE than S
2
as well as all those that have the property (b) are found. In contrast to S
2
, the method of moments estimator is among the latter estimators.</description><subject>Admissibility</subject><subject>Bayes estimators</subject><subject>Error rates</subject><subject>Estimates</subject><subject>Estimation methods</subject><subject>Estimators</subject><subject>Estimators for the mean</subject><subject>Higher education</subject><subject>Mathematical constants</subject><subject>Mean square errors</subject><subject>Method of moments</subject><subject>Population estimates</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>Stein's method</subject><subject>Teacher's Corner</subject><subject>Unbiased estimators</subject><subject>Variance estimation</subject><issn>0003-1305</issn><issn>1537-2731</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEQxYMoWKvfQCHgeesk2W02J6mlVaHVg3-uIZsmmtJu2mRLqZ_eLKsePQ3De28e80PoksCAQAk3AMAIg2JAgdABZwUFcYR6pGA8o5yRY9RrLVnrOUVnMS7TCnxIe2g6wk9mjyexcWvV-IC9xc2nwe8qOFVrg-9UNAvsazx3tVu7L1d_4LlRNX7Z7lRI0iQEH87RiVWraC5-Zh-9TSev44ds9nz_OB7NMs0K3mS8LBdUWGWMVqLgWg1NSUrgwpRGCEaV0oRX1hpKgORW8KrUAJXOrapKzgTro-vu7ib47c7ERi79LtSpUhI6LIbAKcmTK-9cOvgYg7FyE9J74SAJyJaY_CUmW2KyI5ZiV11sGROJvwxljIkCSNJvO93V1oe12vuwWshGHVY-2JBouSjZvw3fivh55Q</recordid><startdate>20121101</startdate><enddate>20121101</enddate><creator>Kourouklis, Stavros</creator><general>Taylor & Francis Group</general><general>American Statistical Association</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20121101</creationdate><title>A New Estimator of the Variance Based on Minimizing Mean Squared Error</title><author>Kourouklis, Stavros</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c357t-788d29faeeca957ca6e818079e8e9932aac17bffe21014f97b8c00bc4fab87393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Admissibility</topic><topic>Bayes estimators</topic><topic>Error rates</topic><topic>Estimates</topic><topic>Estimation methods</topic><topic>Estimators</topic><topic>Estimators for the mean</topic><topic>Higher education</topic><topic>Mathematical constants</topic><topic>Mean square errors</topic><topic>Method of moments</topic><topic>Population estimates</topic><topic>Statistical variance</topic><topic>Statistics</topic><topic>Stein's method</topic><topic>Teacher's Corner</topic><topic>Unbiased estimators</topic><topic>Variance estimation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kourouklis, Stavros</creatorcontrib><collection>CrossRef</collection><jtitle>The American statistician</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kourouklis, Stavros</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A New Estimator of the Variance Based on Minimizing Mean Squared Error</atitle><jtitle>The American statistician</jtitle><date>2012-11-01</date><risdate>2012</risdate><volume>66</volume><issue>4</issue><spage>234</spage><epage>236</epage><pages>234-236</pages><issn>0003-1305</issn><eissn>1537-2731</eissn><coden>ASTAAJ</coden><abstract>In 2005, Yatracos constructed the estimator S
2
2
= c
2
S
2
, c
2
= (n + 2)(n − 1)[n(n + 1)]
− 1
, of the variance, which has smaller mean squared error (MSE) than the unbiased estimator S
2
. In this work, the estimator S
2
1
= c
1
S
2
, c
1
= n(n − 1)[n(n − 1) + 2]
− 1
, is constructed and is shown to have the following properties: (a) it has smaller MSE than S
2
2
, and (b) it cannot be improved in terms of MSE by an estimator of the form cS
2
, c > 0. The method of construction is based on Stein's classical idea brought forward in 1964, is very simple, and may be taught even in an undergraduate class. Also, all the estimators of the form cS
2
, c > 0, with smaller MSE than S
2
as well as all those that have the property (b) are found. In contrast to S
2
, the method of moments estimator is among the latter estimators.</abstract><cop>Alexandria</cop><pub>Taylor & Francis Group</pub><doi>10.1080/00031305.2012.735209</doi><tpages>3</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0003-1305 |
| ispartof | The American statistician, 2012-11, Vol.66 (4), p.234-236 |
| issn | 0003-1305 1537-2731 |
| language | eng |
| recordid | cdi_jstor_primary_23339501 |
| source | Taylor and Francis Science and Technology Collection; JSTOR Archival Journals |
| subjects | Admissibility Bayes estimators Error rates Estimates Estimation methods Estimators Estimators for the mean Higher education Mathematical constants Mean square errors Method of moments Population estimates Statistical variance Statistics Stein's method Teacher's Corner Unbiased estimators Variance estimation |
| title | A New Estimator of the Variance Based on Minimizing Mean Squared Error |
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