Are deviations in a gradually varying mean relevant? A testing approach based on sup-norm estimators

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dc.contributor.authorBücher, Axel
dc.contributor.authorDette, Holger
dc.contributor.authorHeinrichs, Florian
dc.date.accessioned2020-02-19T12:59:46Z
dc.date.available2020-02-19T12:59:46Z
dc.date.issued2020
dc.description.abstractClassical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly non-stationary time series and at (2) identifying regions where the mean exhibits a piecewise constant behavior. In many applications however, it is more reasonable to assume that the mean changes gradually in a smooth way. Those gradual changes may either be non-relevant (i.e., small), or relevant for a specific problem at hand, and the present paper presents statistical methodology to detect the latter. More precisely, we consider the common nonparametric regression model Xi = μ(i/n) +εi with possibly non-stationary errors and propose a test for the null hypothesis that the maximum absolute deviation of the regression function μ from a functional g(μ) (such as the value μ(0) or the integral 1 0 μ(t)dt) is smaller than a given threshold on a given interval [x0, x1] [0, 1]. A test for this type of hypotheses is developed using an appropriate estimator, say ˆ d∞n, for the maximum deviation d∞ = supt∈[x0,x1] |μ(t) − g(μ)|. We derive the limiting distribution of an appropriately standardized version of ˆ d∞,n, where the standardization depends on the Lebesgue measure of the set of extremal points of the function μ(·) − g(μ). A refined procedure based on an estimate of this set is developed and its consistency is proved. The results are illustrated by means of a simulation study and a data example.en
dc.identifier.urihttp://hdl.handle.net/2003/38720
dc.identifier.urihttps://doi.org/10.17877/DE290R-20639
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;3/2020en
dc.subjectrelevant change point analysisen
dc.subjectgradual changesen
dc.subjectmaximum deviationen
dc.subjectlocal-linear estimatoren
dc.subjectGumbel distributionen
dc.subjectGaussian approximationen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.subject.rswkChange-point-Problemde
dc.subject.rswkMaximale Abweichungde
dc.subject.rswkSchätzfunktionde
dc.subject.rswkGauß-Approximationde
dc.titleAre deviations in a gradually varying mean relevant? A testing approach based on sup-norm estimatorsen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access
eldorado.secondarypublicationfalsede

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Sonderforschungsbereich (SFB) 823