A note on martingale transforms for model checks

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dc.contributor.authorBehl, Peter
dc.contributor.authorDette, Holger
dc.contributor.authorVetter, Mathias
dc.date.accessioned2010-05-07T10:25:02Z
dc.date.available2010-05-07T10:25:02Z
dc.date.issued2010-05-07T10:25:02Z
dc.description.abstractMartingale transforms are a well known tool to derive asymptotically distribution free tests for statistics based on empirical processes. Since its introduction by Khmaladze (1981) they have been frequently applied to many testing problems. In this paper martingale transforms for empirical processes are discussed from a non standard perspective with a specific focus on the case where the null hypothesis is not satisfied. For the sake of a transparent presentation we restrict our investigations to the problem of checking model assumptions in regression models, but the conclusions are generally valid. We show the weak convergence of empirical processes under fixed alternatives and introduce a new version of the martingale transform such that the transformed limiting process is a Brownian motion in scaled time, even if the null hypothesis is not satisfied.en
dc.identifier.urihttp://hdl.handle.net/2003/27162
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-8591
dc.language.isoen
dc.relation.ispartofseriesDiscussion Paper / SFB 823 ; 15/2010
dc.subjectmarked empirical processen
dc.subjectMartingale transformen
dc.subjectmodel checken
dc.subjectnonparametric regressionen
dc.subjectweak convergence under fixed alternativesen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleA note on martingale transforms for model checksen
dc.typeText
dc.type.publicationtypereport
dcterms.accessRightsopen access

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