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Article: Estimation of central shapes of error distributions in linear regression problems

TitleEstimation of central shapes of error distributions in linear regression problems
Authors
KeywordsCentre Exponent
L(p) Estimator
Regression
Subsampling
Issue Date2013
Citation
Annals of the Institute of Statistical Mathematics, 2013, v. 65 n. 1, p. 105-124 How to Cite?
AbstractConsider a linear regression model subject to an error distribution which is symmetric about 0 and varies regularly at 0 with exponent ζ. We propose two estimators of ζ, which characterizes the central shape of the error distribution. Both methods are motivated by the well-known Hill estimator, which has been extensively studied in the related problem of estimating tail indices, but substitute reciprocals of small L p residuals for the extreme order statistics in its original definition. The first method requires careful choices of p and the number k of smallest residuals employed for calculating the estimator. The second method is based on subsampling and works under less restrictive conditions on p and k. Both estimators are shown to be consistent for ζ and asymptotically normal. A simulation study is conducted to compare our proposed procedures with alternative estimates of ζ constructed using resampling methods designed for convergence rate estimation. © 2012 The Institute of Statistical Mathematics, Tokyo.
Persistent Identifierhttp://hdl.handle.net/10722/172494
ISSN
2015 Impact Factor: 0.768
2015 SCImago Journal Rankings: 0.931
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLai, PYen_US
dc.contributor.authorLee, SMSen_US
dc.date.accessioned2012-10-30T06:22:47Z-
dc.date.available2012-10-30T06:22:47Z-
dc.date.issued2013en_US
dc.identifier.citationAnnals of the Institute of Statistical Mathematics, 2013, v. 65 n. 1, p. 105-124en_US
dc.identifier.issn0020-3157en_US
dc.identifier.urihttp://hdl.handle.net/10722/172494-
dc.description.abstractConsider a linear regression model subject to an error distribution which is symmetric about 0 and varies regularly at 0 with exponent ζ. We propose two estimators of ζ, which characterizes the central shape of the error distribution. Both methods are motivated by the well-known Hill estimator, which has been extensively studied in the related problem of estimating tail indices, but substitute reciprocals of small L p residuals for the extreme order statistics in its original definition. The first method requires careful choices of p and the number k of smallest residuals employed for calculating the estimator. The second method is based on subsampling and works under less restrictive conditions on p and k. Both estimators are shown to be consistent for ζ and asymptotically normal. A simulation study is conducted to compare our proposed procedures with alternative estimates of ζ constructed using resampling methods designed for convergence rate estimation. © 2012 The Institute of Statistical Mathematics, Tokyo.en_US
dc.languageengen_US
dc.relation.ispartofAnnals of the Institute of Statistical Mathematicsen_US
dc.subjectCentre Exponenten_US
dc.subjectL(p) Estimatoren_US
dc.subjectRegressionen_US
dc.subjectSubsamplingen_US
dc.titleEstimation of central shapes of error distributions in linear regression problemsen_US
dc.typeArticleen_US
dc.identifier.emailLee, SMS: smslee@hku.hken_US
dc.identifier.authorityLee, SMS=rp00726en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1007/s10463-012-0360-2en_US
dc.identifier.scopuseid_2-s2.0-84872300311en_US
dc.identifier.hkuros215272-
dc.identifier.spage105en_US
dc.identifier.epage124en_US
dc.identifier.isiWOS:000313015000006-
dc.publisher.placeGermanyen_US
dc.identifier.scopusauthoridLai, PY=8629588700en_US
dc.identifier.scopusauthoridLee, SMS=24280225500en_US
dc.identifier.citeulike10632324-

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