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Article: Estimation of central shapes of error distributions in linear regression problems
Title | Estimation of central shapes of error distributions in linear regression problems |
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Authors | |
Keywords | Centre Exponent L(p) Estimator Regression Subsampling |
Issue Date | 2013 |
Citation | Annals of the Institute of Statistical Mathematics, 2013, v. 65 n. 1, p. 105-124 How to Cite? |
Abstract | Consider 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 Identifier | http://hdl.handle.net/10722/172494 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 0.791 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Lai, PY | en_US |
dc.contributor.author | Lee, SMS | en_US |
dc.date.accessioned | 2012-10-30T06:22:47Z | - |
dc.date.available | 2012-10-30T06:22:47Z | - |
dc.date.issued | 2013 | en_US |
dc.identifier.citation | Annals of the Institute of Statistical Mathematics, 2013, v. 65 n. 1, p. 105-124 | en_US |
dc.identifier.issn | 0020-3157 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/172494 | - |
dc.description.abstract | Consider 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.language | eng | en_US |
dc.relation.ispartof | Annals of the Institute of Statistical Mathematics | en_US |
dc.subject | Centre Exponent | en_US |
dc.subject | L(p) Estimator | en_US |
dc.subject | Regression | en_US |
dc.subject | Subsampling | en_US |
dc.title | Estimation of central shapes of error distributions in linear regression problems | en_US |
dc.type | Article | en_US |
dc.identifier.email | Lee, SMS: smslee@hku.hk | en_US |
dc.identifier.authority | Lee, SMS=rp00726 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1007/s10463-012-0360-2 | en_US |
dc.identifier.scopus | eid_2-s2.0-84872300311 | en_US |
dc.identifier.hkuros | 215272 | - |
dc.identifier.spage | 105 | en_US |
dc.identifier.epage | 124 | en_US |
dc.identifier.isi | WOS:000313015000006 | - |
dc.publisher.place | Germany | en_US |
dc.identifier.scopusauthorid | Lai, PY=8629588700 | en_US |
dc.identifier.scopusauthorid | Lee, SMS=24280225500 | en_US |
dc.identifier.citeulike | 10632324 | - |
dc.identifier.issnl | 0020-3157 | - |