Testing discontinuities in nonparametric regression

Handle URI:
http://hdl.handle.net/10754/623053
Title:
Testing discontinuities in nonparametric regression
Authors:
Dai, Wenlin; Zhou, Yuejin; Tong, Tiejun
Abstract:
In nonparametric regression, it is often needed to detect whether there are jump discontinuities in the mean function. In this paper, we revisit the difference-based method in [13 H.-G. Müller and U. Stadtmüller, Discontinuous versus smooth regression, Ann. Stat. 27 (1999), pp. 299–337. doi: 10.1214/aos/1018031100]] and propose to further improve it. To achieve the goal, we first reveal that their method is less efficient due to the inappropriate choice of the response variable in their linear regression model. We then propose a new regression model for estimating the residual variance and the total amount of discontinuities simultaneously. In both theory and simulation, we show that the proposed variance estimator has a smaller mean-squared error compared to the existing estimator, whereas the estimation efficiency for the total amount of discontinuities remains unchanged. Finally, we construct a new test procedure for detection of discontinuities using the proposed method; and via simulation studies, we demonstrate that our new test procedure outperforms the existing one in most settings.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Dai W, Zhou Y, Tong T (2017) Testing discontinuities in nonparametric regression. Journal of Applied Statistics: 1–24. Available: http://dx.doi.org/10.1080/02664763.2017.1280004.
Publisher:
Informa UK Limited
Journal:
Journal of Applied Statistics
Issue Date:
19-Jan-2017
DOI:
10.1080/02664763.2017.1280004
Type:
Article
ISSN:
0266-4763; 1360-0532
Sponsors:
Tiejun Tong’s research was supported by the Hong Kong Baptist University grants FRG1/14-15/044, FRG2/15-16/019 and FRG2/15-16/038, and the National Natural Science Foundation of China grant (No. 11671338).
Additional Links:
http://www.tandfonline.com/doi/full/10.1080/02664763.2017.1280004
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorDai, Wenlinen
dc.contributor.authorZhou, Yuejinen
dc.contributor.authorTong, Tiejunen
dc.date.accessioned2017-03-20T12:44:54Z-
dc.date.available2017-03-20T12:44:54Z-
dc.date.issued2017-01-19en
dc.identifier.citationDai W, Zhou Y, Tong T (2017) Testing discontinuities in nonparametric regression. Journal of Applied Statistics: 1–24. Available: http://dx.doi.org/10.1080/02664763.2017.1280004.en
dc.identifier.issn0266-4763en
dc.identifier.issn1360-0532en
dc.identifier.doi10.1080/02664763.2017.1280004en
dc.identifier.urihttp://hdl.handle.net/10754/623053-
dc.description.abstractIn nonparametric regression, it is often needed to detect whether there are jump discontinuities in the mean function. In this paper, we revisit the difference-based method in [13 H.-G. Müller and U. Stadtmüller, Discontinuous versus smooth regression, Ann. Stat. 27 (1999), pp. 299–337. doi: 10.1214/aos/1018031100]] and propose to further improve it. To achieve the goal, we first reveal that their method is less efficient due to the inappropriate choice of the response variable in their linear regression model. We then propose a new regression model for estimating the residual variance and the total amount of discontinuities simultaneously. In both theory and simulation, we show that the proposed variance estimator has a smaller mean-squared error compared to the existing estimator, whereas the estimation efficiency for the total amount of discontinuities remains unchanged. Finally, we construct a new test procedure for detection of discontinuities using the proposed method; and via simulation studies, we demonstrate that our new test procedure outperforms the existing one in most settings.en
dc.description.sponsorshipTiejun Tong’s research was supported by the Hong Kong Baptist University grants FRG1/14-15/044, FRG2/15-16/019 and FRG2/15-16/038, and the National Natural Science Foundation of China grant (No. 11671338).en
dc.publisherInforma UK Limiteden
dc.relation.urlhttp://www.tandfonline.com/doi/full/10.1080/02664763.2017.1280004en
dc.rightsThis is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Applied Statistics on 19 Jan 2017, available online: http://wwww.tandfonline.com/10.1080/02664763.2017.1280004.en
dc.subjectAsymptotic normalityen
dc.subjectdifference-based estimatoren
dc.subjectjump pointen
dc.subjectmodel selectionen
dc.subjectnonparametric regressionen
dc.subjectresidual varianceen
dc.titleTesting discontinuities in nonparametric regressionen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Applied Statisticsen
dc.eprint.versionPost-printen
dc.contributor.institutionHKBU Institute of Research and Continuing Education, Shenzhen, People’s Republic of Chinaen
dc.contributor.institutionSchool of Mathematics and Statistics, Zhejiang Gongshang University, Hangzhou, People’s Republic of Chinaen
dc.contributor.institutionDepartment of Mathematics, Hong Kong Baptist University, Hong Kongen
kaust.authorDai, Wenlinen
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