Edgeworth expansions and normalizing transforms for inequality measures
Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measur...
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| Veröffentlicht in: | Econometrics 2009-05, Vol.150 (1), p.16-29 |
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| creator | Schluter, Christian van Garderen, Kees Jan |
| description | Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate
O
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. This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order
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. We illustrate our procedure with an application to regional inequality measurement in Côte d’Ivoire. |
| doi_str_mv | 10.1016/j.jeconom.2008.12.022 |
| format | Article |
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O
(
n
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1
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. This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order
O
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2
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. We illustrate our procedure with an application to regional inequality measurement in Côte d’Ivoire.</description><identifier>ISSN: 0304-4076</identifier><identifier>ISSN: 2225-1146</identifier><identifier>EISSN: 1872-6895</identifier><identifier>EISSN: 2225-1146</identifier><identifier>DOI: 10.1016/j.jeconom.2008.12.022</identifier><identifier>CODEN: JECMB6</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Applications ; Asymptotic methods ; Bootstrap method ; Confidence intervals ; Distribution theory ; Entropy ; Exact sciences and technology ; Experimental design ; Generalized Entropy inequality measures ; Generalized Entropy inequality measures Higher- order expansions Normalizing transformations ; Higher- order expansions ; Income inequality ; Inequality ; Insurance, economics, finance ; Macroeconomics ; Mathematics ; Normal distribution ; Normalizing transformations ; Probability and statistics ; Probability theory and stochastic processes ; Sciences and techniques of general use ; Statistical models ; Statistics ; Studies</subject><ispartof>Econometrics, 2009-05, Vol.150 (1), p.16-29</ispartof><rights>2009 Elsevier B.V.</rights><rights>2009 INIST-CNRS</rights><rights>Copyright Elsevier Sequoia S.A. May 2009</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c606t-3dc039a1ff7736d8b14a1d4c156f4c3f73aab8eb73984041bde82e9cc971cafb3</citedby><cites>FETCH-LOGICAL-c606t-3dc039a1ff7736d8b14a1d4c156f4c3f73aab8eb73984041bde82e9cc971cafb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.jeconom.2008.12.022$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,780,784,885,3550,4008,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21516385$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/eeeeconom/v_3a150_3ay_3a2009_3ai_3a1_3ap_3a16-29.htm$$DView record in RePEc$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-00565100$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Schluter, Christian</creatorcontrib><creatorcontrib>van Garderen, Kees Jan</creatorcontrib><title>Edgeworth expansions and normalizing transforms for inequality measures</title><title>Econometrics</title><description>Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate
O
(
n
−
1
)
. This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order
O
(
n
−
3
/
2
)
. We illustrate our procedure with an application to regional inequality measurement in Côte d’Ivoire.</description><subject>Applications</subject><subject>Asymptotic methods</subject><subject>Bootstrap method</subject><subject>Confidence intervals</subject><subject>Distribution theory</subject><subject>Entropy</subject><subject>Exact sciences and technology</subject><subject>Experimental design</subject><subject>Generalized Entropy inequality measures</subject><subject>Generalized Entropy inequality measures Higher- order expansions Normalizing transformations</subject><subject>Higher- order expansions</subject><subject>Income inequality</subject><subject>Inequality</subject><subject>Insurance, economics, finance</subject><subject>Macroeconomics</subject><subject>Mathematics</subject><subject>Normal distribution</subject><subject>Normalizing transformations</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Sciences and techniques of general use</subject><subject>Statistical models</subject><subject>Statistics</subject><subject>Studies</subject><issn>0304-4076</issn><issn>2225-1146</issn><issn>1872-6895</issn><issn>2225-1146</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqFkU2L3DAMhkNpodNtf0IhFFroIakdJ7ZzKsuyXzDQS3s2jqPsOCR21k6mnf76Vcgwh15qkATSI1niTZKPlOSUUP6tz3sw3vkxLwiROS1yUhSvkh2Vosi4rKvXyY4wUmYlEfxt8i7GnhBSlZLtkvvb9gl--zAfUvgzaRetdzHVrk2dD6Me7F_rntI5YKXDREzRp9bB84K1-ZSOoOMSIL5P3nR6iPDhHK-SX3e3P28esv2P-8eb631mOOFzxlpDWK1p1wnBeCsbWmraloZWvCsN6wTTupHQCFbLkpS0aUEWUBtTC2p017Cr5Os296AHNQU76nBSXlv1cL1Xaw4P4xUl5EiR_bKxU_DPC8RZjTYaGAbtwC9RMUG5EIVA8NM_YO-X4PAORWvOuaxIjVC1QSb4GAN0l-8pUasOqldnHdSqg6KFQh2w73HrCzCBuTQBvg0-KqZpRdCf0LC1xmDXJNq0Rq6KWh3mEWd9Pi-qo9FDh7IYGy8zC1pRzmSF3PeNA5TiaCGoaCw4A60NYGbVevufrV8AzyG52w</recordid><startdate>20090501</startdate><enddate>20090501</enddate><creator>Schluter, Christian</creator><creator>van Garderen, Kees Jan</creator><general>Elsevier B.V</general><general>Elsevier</general><general>Elsevier Sequoia S.A</general><general>MDPI</general><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>20090501</creationdate><title>Edgeworth expansions and normalizing transforms for inequality measures</title><author>Schluter, Christian ; van Garderen, Kees Jan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c606t-3dc039a1ff7736d8b14a1d4c156f4c3f73aab8eb73984041bde82e9cc971cafb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Applications</topic><topic>Asymptotic methods</topic><topic>Bootstrap method</topic><topic>Confidence intervals</topic><topic>Distribution theory</topic><topic>Entropy</topic><topic>Exact sciences and technology</topic><topic>Experimental design</topic><topic>Generalized Entropy inequality measures</topic><topic>Generalized Entropy inequality measures Higher- order expansions Normalizing transformations</topic><topic>Higher- order expansions</topic><topic>Income inequality</topic><topic>Inequality</topic><topic>Insurance, economics, finance</topic><topic>Macroeconomics</topic><topic>Mathematics</topic><topic>Normal distribution</topic><topic>Normalizing transformations</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Sciences and techniques of general use</topic><topic>Statistical models</topic><topic>Statistics</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schluter, Christian</creatorcontrib><creatorcontrib>van Garderen, Kees Jan</creatorcontrib><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Econometrics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schluter, Christian</au><au>van Garderen, Kees Jan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Edgeworth expansions and normalizing transforms for inequality measures</atitle><jtitle>Econometrics</jtitle><date>2009-05-01</date><risdate>2009</risdate><volume>150</volume><issue>1</issue><spage>16</spage><epage>29</epage><pages>16-29</pages><issn>0304-4076</issn><issn>2225-1146</issn><eissn>1872-6895</eissn><eissn>2225-1146</eissn><coden>JECMB6</coden><abstract>Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate
O
(
n
−
1
)
. This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order
O
(
n
−
3
/
2
)
. We illustrate our procedure with an application to regional inequality measurement in Côte d’Ivoire.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.jeconom.2008.12.022</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Econometrics, 2009-05, Vol.150 (1), p.16-29 |
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| source | RePEc; Access via ScienceDirect (Elsevier) |
| subjects | Applications Asymptotic methods Bootstrap method Confidence intervals Distribution theory Entropy Exact sciences and technology Experimental design Generalized Entropy inequality measures Generalized Entropy inequality measures Higher- order expansions Normalizing transformations Higher- order expansions Income inequality Inequality Insurance, economics, finance Macroeconomics Mathematics Normal distribution Normalizing transformations Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Statistical models Statistics Studies |
| title | Edgeworth expansions and normalizing transforms for inequality measures |
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