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Article: On bandwidth selection in local polynomial regression analysis and its application to multi-resolution analysis of non-uniform data

TitleOn bandwidth selection in local polynomial regression analysis and its application to multi-resolution analysis of non-uniform data
Authors
KeywordsAdaptive bandwidth selection
Intersection of confidence intervals
Local polynomial regression
Non-uniformly sampled data analysis
Wavelet
Issue Date2008
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/content/120889/
Citation
Journal Of Signal Processing Systems, 2008, v. 52 n. 3, p. 263-280 How to Cite?
AbstractThis paper studies adaptive bandwidth selection method for local polynomial regression (LPR) and its application to multi-resolution analysis (MRA) of non-uniformly sampled data. In LPR, the observations are modeled locally by a polynomial using least-squares criterion with a kernel having a certain support or bandwidth so that a better bias-variance tradeoff can be achieved. In this paper, two bandwidth selection methods, namely the Fan and Gijbels's bandwidth selection (FGBS) method (Fan and Gijbels, Local Polynomial Modelling and Its Applications, Chapman and Hall, London, 1996; Fan and Gijbels, Stat Sin 57:371-394, 1995) in the statistical community and the intersection of confidence intervals (ICI) method commonly used in the signal and image processing communities, are reviewed and compared in terms of their performance and implementation complexity using standard testing data sets. Furthermore, using the result of Stankovi (IEEE Trans Signal Proc 52:1228-1234, 2004), a new refined ICI-based adaptive bandwidth selection method for LPR and its associated reliability analysis are proposed. In addition, recursive implementations of LPR with the two classes of bandwidth selection methods are considered for online applications. Simulation results show that the performances of the FGBS method and the refined ICI method are comparable for the data sets tested. Since LPR with adaptive bandwidths can be naturally applied to non-uniformly sampled noisy observations, we propose to use it as a pre-processing step to a conventional MRA so that a MRA of non-uniformly sampled data can be realized. Simulation results show that the proposed LPR-based MRA gives better results than conventional linear interpolation of the data. © 2008 Springer Science+Business Media, LLC.
Persistent Identifierhttp://hdl.handle.net/10722/58723
ISSN
2015 Impact Factor: 0.508
2015 SCImago Journal Rankings: 0.262
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorZhang, ZGen_HK
dc.contributor.authorChan, SCen_HK
dc.contributor.authorHo, KLen_HK
dc.contributor.authorHo, KCen_HK
dc.date.accessioned2010-05-31T03:35:46Z-
dc.date.available2010-05-31T03:35:46Z-
dc.date.issued2008en_HK
dc.identifier.citationJournal Of Signal Processing Systems, 2008, v. 52 n. 3, p. 263-280en_HK
dc.identifier.issn1939-8018en_HK
dc.identifier.urihttp://hdl.handle.net/10722/58723-
dc.description.abstractThis paper studies adaptive bandwidth selection method for local polynomial regression (LPR) and its application to multi-resolution analysis (MRA) of non-uniformly sampled data. In LPR, the observations are modeled locally by a polynomial using least-squares criterion with a kernel having a certain support or bandwidth so that a better bias-variance tradeoff can be achieved. In this paper, two bandwidth selection methods, namely the Fan and Gijbels's bandwidth selection (FGBS) method (Fan and Gijbels, Local Polynomial Modelling and Its Applications, Chapman and Hall, London, 1996; Fan and Gijbels, Stat Sin 57:371-394, 1995) in the statistical community and the intersection of confidence intervals (ICI) method commonly used in the signal and image processing communities, are reviewed and compared in terms of their performance and implementation complexity using standard testing data sets. Furthermore, using the result of Stankovi (IEEE Trans Signal Proc 52:1228-1234, 2004), a new refined ICI-based adaptive bandwidth selection method for LPR and its associated reliability analysis are proposed. In addition, recursive implementations of LPR with the two classes of bandwidth selection methods are considered for online applications. Simulation results show that the performances of the FGBS method and the refined ICI method are comparable for the data sets tested. Since LPR with adaptive bandwidths can be naturally applied to non-uniformly sampled noisy observations, we propose to use it as a pre-processing step to a conventional MRA so that a MRA of non-uniformly sampled data can be realized. Simulation results show that the proposed LPR-based MRA gives better results than conventional linear interpolation of the data. © 2008 Springer Science+Business Media, LLC.en_HK
dc.languageengen_HK
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/content/120889/en_HK
dc.relation.ispartofJournal of Signal Processing Systemsen_HK
dc.subjectAdaptive bandwidth selectionen_HK
dc.subjectIntersection of confidence intervalsen_HK
dc.subjectLocal polynomial regressionen_HK
dc.subjectNon-uniformly sampled data analysisen_HK
dc.subjectWaveleten_HK
dc.titleOn bandwidth selection in local polynomial regression analysis and its application to multi-resolution analysis of non-uniform dataen_HK
dc.typeArticleen_HK
dc.identifier.emailZhang, ZG:zgzhang@eee.hku.hken_HK
dc.identifier.emailChan, SC:scchan@eee.hku.hken_HK
dc.identifier.emailHo, KL:klho@eee.hku.hken_HK
dc.identifier.authorityZhang, ZG=rp01565en_HK
dc.identifier.authorityChan, SC=rp00094en_HK
dc.identifier.authorityHo, KL=rp00117en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s11265-007-0156-4en_HK
dc.identifier.scopuseid_2-s2.0-46249116711en_HK
dc.identifier.hkuros159398en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-46249116711&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume52en_HK
dc.identifier.issue3en_HK
dc.identifier.spage263en_HK
dc.identifier.epage280en_HK
dc.identifier.isiWOS:000257226700004-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridZhang, ZG=8597618700en_HK
dc.identifier.scopusauthoridChan, SC=13310287100en_HK
dc.identifier.scopusauthoridHo, KL=7403581592en_HK
dc.identifier.scopusauthoridHo, KC=7403581344en_HK

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