
Change point analysis in nonstationary processes  a mass excess approach
This paper considers the problem of testing if a sequence of means (μ_t)...
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Testing relevant hypotheses in functional time series via selfnormalization
In this paper we develop methodology for testing relevant hypotheses in ...
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Change Point Analysis of Correlation in Nonstationary Time Series
A restrictive assumption in change point analysis is "stationarity under...
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Nuisance Parameters Free Changepoint Detection in Nonstationary Series
Detecting abrupt changes in the mean of a time series, socalled changep...
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Changepoint in Linear Relations
Linear relations, containing measurement errors in input and output data...
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Identifying shifts between two regression curves
This article studies the problem whether two convex (concave) regression...
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A breakpoint detection in the mean model with heterogeneous variance on fixed timeintervals
This work is motivated by an application for the homogeneization of GNSS...
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Are deviations in a gradually varying mean relevant? A testing approach based on supnorm estimators
Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly nonstationary 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 nonrelevant (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 X_i = μ (i/n) + ε_i with possibly nonstationary 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 ∫_0^1μ (t) dt) is smaller than a given threshold on a given interval [x_0,x_1] ⊆ [0,1]. A test for this type of hypotheses is developed using an appropriate estimator, say d̂_∞, n, for the maximum deviation d_∞= sup_t ∈ [x_0,x_1] μ (t)  g( μ) . We derive the limiting distribution of an appropriately standardized version of d̂_∞,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.
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