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Article: On the local polynomial estimators of the counting process intensity function and its derivatives

TitleOn the local polynomial estimators of the counting process intensity function and its derivatives
Authors
KeywordsAutomatic boundary correction
Boundary effects
Change point
Counting process
Derivative estimation
Effective kernel
Equivalent kernel
Hazard rate
Intensity function
Kernel smoothing
Local polynomial
Martingale estimating equation
Multiplicative intensity model
Non-parametric estimation
Seismology
Sichuan earthquake
Survival analysis
Issue Date2011
PublisherBlackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/SJOS
Citation
Scandinavian Journal Of Statistics, 2011, v. 38 n. 4, p. 631-649 How to Cite?
AbstractWe consider the properties of the local polynomial estimators of a counting process intensity function and its derivatives. By expressing the local polynomial estimators in a kernel smoothing form via effective kernels, we show that the bias and variance of the estimators at boundary points are of the same magnitude as at interior points and therefore the local polynomial estimators in the context of intensity estimation also enjoy the automatic boundary correction property as they do in other contexts such as regression. The asymptotically optimal bandwidths and optimal kernel functions are obtained through the asymptotic expressions of the mean square error of the estimators. For practical purpose, we suggest an effective and easy-to-calculate data-driven bandwidth selector. Simulation studies are carried out to assess the performance of the local polynomial estimators and the proposed bandwidth selector. The estimators and the bandwidth selector are applied to estimate the rate of aftershocks of the Sichuan earthquake and the rate of the Personal Emergency Link calls in Hong Kong. © 2011 Board of the Foundation of the Scandinavian Journal of Statistics.
Persistent Identifierhttp://hdl.handle.net/10722/159874
ISSN
2015 Impact Factor: 0.908
2015 SCImago Journal Rankings: 1.362
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChen, Fen_HK
dc.contributor.authorYip, PSFen_HK
dc.contributor.authorLam, KFen_HK
dc.date.accessioned2012-08-16T05:58:25Z-
dc.date.available2012-08-16T05:58:25Z-
dc.date.issued2011en_HK
dc.identifier.citationScandinavian Journal Of Statistics, 2011, v. 38 n. 4, p. 631-649en_HK
dc.identifier.issn0303-6898en_HK
dc.identifier.urihttp://hdl.handle.net/10722/159874-
dc.description.abstractWe consider the properties of the local polynomial estimators of a counting process intensity function and its derivatives. By expressing the local polynomial estimators in a kernel smoothing form via effective kernels, we show that the bias and variance of the estimators at boundary points are of the same magnitude as at interior points and therefore the local polynomial estimators in the context of intensity estimation also enjoy the automatic boundary correction property as they do in other contexts such as regression. The asymptotically optimal bandwidths and optimal kernel functions are obtained through the asymptotic expressions of the mean square error of the estimators. For practical purpose, we suggest an effective and easy-to-calculate data-driven bandwidth selector. Simulation studies are carried out to assess the performance of the local polynomial estimators and the proposed bandwidth selector. The estimators and the bandwidth selector are applied to estimate the rate of aftershocks of the Sichuan earthquake and the rate of the Personal Emergency Link calls in Hong Kong. © 2011 Board of the Foundation of the Scandinavian Journal of Statistics.en_HK
dc.languageengen_US
dc.publisherBlackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/SJOSen_HK
dc.relation.ispartofScandinavian Journal of Statisticsen_HK
dc.subjectAutomatic boundary correctionen_HK
dc.subjectBoundary effectsen_HK
dc.subjectChange pointen_HK
dc.subjectCounting processen_HK
dc.subjectDerivative estimationen_HK
dc.subjectEffective kernelen_HK
dc.subjectEquivalent kernelen_HK
dc.subjectHazard rateen_HK
dc.subjectIntensity functionen_HK
dc.subjectKernel smoothingen_HK
dc.subjectLocal polynomialen_HK
dc.subjectMartingale estimating equationen_HK
dc.subjectMultiplicative intensity modelen_HK
dc.subjectNon-parametric estimationen_HK
dc.subjectSeismologyen_HK
dc.subjectSichuan earthquakeen_HK
dc.subjectSurvival analysisen_HK
dc.titleOn the local polynomial estimators of the counting process intensity function and its derivativesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1467-9469&volume=38&issue=4&spage=631&epage=649&date=2011&atitle=On+the+Local+Polynomial+Estimators+of+the+Counting+Process+Intensity+Function+and+its+Derivativesen_US
dc.identifier.emailYip, PSF: sfpyip@hku.hken_HK
dc.identifier.emailLam, KF: hrntlkf@hkucc.hku.hken_HK
dc.identifier.authorityYip, PSF=rp00596en_HK
dc.identifier.authorityLam, KF=rp00718en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1111/j.1467-9469.2011.00733.xen_HK
dc.identifier.scopuseid_2-s2.0-81855194379en_HK
dc.identifier.hkuros205580en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-81855194379&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume38en_HK
dc.identifier.issue4en_HK
dc.identifier.spage631en_HK
dc.identifier.epage649en_HK
dc.identifier.eissn1467-9469-
dc.identifier.isiWOS:000297841000002-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridChen, F=25928259900en_HK
dc.identifier.scopusauthoridYip, PSF=7102503720en_HK
dc.identifier.scopusauthoridLam, KF=8948421200en_HK

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