دورية أكاديمية
Change-Points in Nonparametric Regression Analysis
| العنوان: | Change-Points in Nonparametric Regression Analysis |
|---|---|
| المؤلفون: | Muller, Hans-Georg |
| بيانات النشر: | The Institute of Mathematical Statistics |
| سنة النشر: | 1992 |
| المجموعة: | Project Euclid (Cornell University Library) |
| مصطلحات موضوعية: | Boundary kernel, change of slope, curve fitting, discontinuity, end-point, functional limit theorem, jump size, kernel estimation, $L^p$ convergence, Nile data, smoothing, weak convergence, 62G05, 62G20 |
| الوصف: | Estimators for location and size of a discontinuity or change-point in an otherwise smooth regression model are proposed. The assumptions needed are much weaker than those made in parametric models. The proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change-points of slope and of higher order curvature. The proposed estimators are based on a comparison of left and right one-sided kernel smoothers. Weak convergence of a stochastic process in local differences to a Gaussian process is established for properly scaled versions of estimators of the location of a change-point. The continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change-point estimators. These rates are typically faster than $n^{-1/2}$. Rates of global $L^p$ convergence of curve estimates with appropriate kernel modifications adapting to estimated change-points are derived as a consequence. It is shown that these rates of convergence are the same as if the location of the change-point was known. The methods are illustrated by means of the well known data on the annual flow volume of the Nile river between 1871 and 1970. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0090-5364 |
| العلاقة: | http://projecteuclid.org/euclid.aos/1176348654Test; Ann. Statist. 20, no. 2 (1992), 737-761 |
| DOI: | 10.1214/aos/1176348654 |
| الإتاحة: | https://doi.org/10.1214/aos/1176348654Test http://projecteuclid.org/euclid.aos/1176348654Test |
| حقوق: | Copyright 1992 Institute of Mathematical Statistics |
| رقم الانضمام: | edsbas.4D61E293 |
| قاعدة البيانات: | BASE |
Full Text Finder | ResultId |
1 |
|---|---|
| Header |
edsbas BASE edsbas.4D61E293 746 3 Academic Journal academicJournal 745.809631347656 |
| PLink |
https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&scope=site&db=edsbas&AN=edsbas.4D61E293&custid=s6537998&authtype=sso |
| FullText |
Array
(
[Availability] => 0
)
Array ( [0] => Array ( [Url] => https://doi.org/10.1214/aos/1176348654# [Name] => EDS - BASE [Category] => fullText [Text] => View record in BASE [MouseOverText] => View record in BASE ) [1] => Array ( [Url] => https://resolver.ebscohost.com/openurl?custid=s6537998&groupid=main&authtype=ip,guest&sid=EBSCO:edsbas&genre=article&issn=00905364&ISBN=&volume=&issue=&date=19920101&spage=&pages=&title=Change-Points in Nonparametric Regression Analysis&atitle=Change-Points%20in%20Nonparametric%20Regression%20Analysis&id=DOI:10.1214/aos/1176348654 [Name] => Full Text Finder (s6537998api) [Category] => fullText [Text] => Full Text Finder [Icon] => https://imageserver.ebscohost.com/branding/images/FTF.gif [MouseOverText] => Full Text Finder ) ) |
| Items |
Array
(
[Name] => Title
[Label] => Title
[Group] => Ti
[Data] => Change-Points in Nonparametric Regression Analysis
)
Array ( [Name] => Author [Label] => Authors [Group] => Au [Data] => <searchLink fieldCode="AR" term="%22Muller%2C+Hans-Georg%22">Muller, Hans-Georg</searchLink> ) Array ( [Name] => Publisher [Label] => Publisher Information [Group] => PubInfo [Data] => The Institute of Mathematical Statistics ) Array ( [Name] => DatePubCY [Label] => Publication Year [Group] => Date [Data] => 1992 ) Array ( [Name] => Subset [Label] => Collection [Group] => HoldingsInfo [Data] => Project Euclid (Cornell University Library) ) Array ( [Name] => Subject [Label] => Subject Terms [Group] => Su [Data] => <searchLink fieldCode="DE" term="%22Boundary+kernel%22">Boundary kernel</searchLink><br /><searchLink fieldCode="DE" term="%22change+of+slope%22">change of slope</searchLink><br /><searchLink fieldCode="DE" term="%22curve+fitting%22">curve fitting</searchLink><br /><searchLink fieldCode="DE" term="%22discontinuity%22">discontinuity</searchLink><br /><searchLink fieldCode="DE" term="%22end-point%22">end-point</searchLink><br /><searchLink fieldCode="DE" term="%22functional+limit+theorem%22">functional limit theorem</searchLink><br /><searchLink fieldCode="DE" term="%22jump+size%22">jump size</searchLink><br /><searchLink fieldCode="DE" term="%22kernel+estimation%22">kernel estimation</searchLink><br /><searchLink fieldCode="DE" term="%22%24L^p%24+convergence%22">$L^p$ convergence</searchLink><br /><searchLink fieldCode="DE" term="%22Nile+data%22">Nile data</searchLink><br /><searchLink fieldCode="DE" term="%22smoothing%22">smoothing</searchLink><br /><searchLink fieldCode="DE" term="%22weak+convergence%22">weak convergence</searchLink><br /><searchLink fieldCode="DE" term="%2262G05%22">62G05</searchLink><br /><searchLink fieldCode="DE" term="%2262G20%22">62G20</searchLink> ) Array ( [Name] => Abstract [Label] => Description [Group] => Ab [Data] => Estimators for location and size of a discontinuity or change-point in an otherwise smooth regression model are proposed. The assumptions needed are much weaker than those made in parametric models. The proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change-points of slope and of higher order curvature. The proposed estimators are based on a comparison of left and right one-sided kernel smoothers. Weak convergence of a stochastic process in local differences to a Gaussian process is established for properly scaled versions of estimators of the location of a change-point. The continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change-point estimators. These rates are typically faster than $n^{-1/2}$. Rates of global $L^p$ convergence of curve estimates with appropriate kernel modifications adapting to estimated change-points are derived as a consequence. It is shown that these rates of convergence are the same as if the location of the change-point was known. The methods are illustrated by means of the well known data on the annual flow volume of the Nile river between 1871 and 1970. ) Array ( [Name] => TypeDocument [Label] => Document Type [Group] => TypDoc [Data] => text ) Array ( [Name] => Format [Label] => File Description [Group] => SrcInfo [Data] => application/pdf ) Array ( [Name] => Language [Label] => Language [Group] => Lang [Data] => English ) Array ( [Name] => ISSN [Label] => ISSN [Group] => ISSN [Data] => 0090-5364 ) Array ( [Name] => NoteTitleSource [Label] => Relation [Group] => SrcInfo [Data] => http://projecteuclid.org/euclid.aos/1176348654; Ann. Statist. 20, no. 2 (1992), 737-761 ) Array ( [Name] => DOI [Label] => DOI [Group] => ID [Data] => 10.1214/aos/1176348654 ) Array ( [Name] => URL [Label] => Availability [Group] => URL [Data] => https://doi.org/10.1214/aos/1176348654<br />http://projecteuclid.org/euclid.aos/1176348654 ) Array ( [Name] => Copyright [Label] => Rights [Group] => Cpyrght [Data] => Copyright 1992 Institute of Mathematical Statistics ) Array ( [Name] => AN [Label] => Accession Number [Group] => ID [Data] => edsbas.4D61E293 ) |
| RecordInfo |
Array
(
[BibEntity] => Array
(
[Identifiers] => Array
(
[0] => Array
(
[Type] => doi
[Value] => 10.1214/aos/1176348654
)
)
[Languages] => Array
(
[0] => Array
(
[Text] => English
)
)
[Subjects] => Array
(
[0] => Array
(
[SubjectFull] => Boundary kernel
[Type] => general
)
[1] => Array
(
[SubjectFull] => change of slope
[Type] => general
)
[2] => Array
(
[SubjectFull] => curve fitting
[Type] => general
)
[3] => Array
(
[SubjectFull] => discontinuity
[Type] => general
)
[4] => Array
(
[SubjectFull] => end-point
[Type] => general
)
[5] => Array
(
[SubjectFull] => functional limit theorem
[Type] => general
)
[6] => Array
(
[SubjectFull] => jump size
[Type] => general
)
[7] => Array
(
[SubjectFull] => kernel estimation
[Type] => general
)
[8] => Array
(
[SubjectFull] => $L^p$ convergence
[Type] => general
)
[9] => Array
(
[SubjectFull] => Nile data
[Type] => general
)
[10] => Array
(
[SubjectFull] => smoothing
[Type] => general
)
[11] => Array
(
[SubjectFull] => weak convergence
[Type] => general
)
[12] => Array
(
[SubjectFull] => 62G05
[Type] => general
)
[13] => Array
(
[SubjectFull] => 62G20
[Type] => general
)
)
[Titles] => Array
(
[0] => Array
(
[TitleFull] => Change-Points in Nonparametric Regression Analysis
[Type] => main
)
)
)
[BibRelationships] => Array
(
[HasContributorRelationships] => Array
(
[0] => Array
(
[PersonEntity] => Array
(
[Name] => Array
(
[NameFull] => Muller, Hans-Georg
)
)
)
)
[IsPartOfRelationships] => Array
(
[0] => Array
(
[BibEntity] => Array
(
[Dates] => Array
(
[0] => Array
(
[D] => 01
[M] => 01
[Type] => published
[Y] => 1992
)
)
[Identifiers] => Array
(
[0] => Array
(
[Type] => issn-print
[Value] => 00905364
)
[1] => Array
(
[Type] => issn-locals
[Value] => edsbas
)
)
)
)
)
)
)
|
| IllustrationInfo |