Authors: | Bücher, Axel Dette, Holger Heinrichs, Florian |
Title: | Are deviations in a gradually varying mean relevant? A testing approach based on sup-norm estimators |
Language (ISO): | en |
Abstract: | Classical 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. |
Subject Headings: | relevant change point analysis gradual changes maximum deviation local-linear estimator Gumbel distribution Gaussian approximation |
Subject Headings (RSWK): | Change-point-Problem Maximale Abweichung Schätzfunktion Gauß-Approximation |
URI: | http://hdl.handle.net/2003/38720 https://doi.org/10.17877/DE290R-20639 |
Issue Date: | 2020 |
Appears in Collections: | Sonderforschungsbereich (SFB) 823 |
Files in This Item:
File | Description | Size | Format | |
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DP_0320_SFB823_Bücher_Dette_Heinrichs.pdf | DNB | 658.89 kB | Adobe PDF | View/Open |
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