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2017 Power of change-point tests for long-range dependent data
Herold Dehling, Aeneas Rooch, Murad S. Taqqu
Electron. J. Statist. 11(1): 2168-2198 (2017). DOI: 10.1214/17-EJS1283

Abstract

We investigate the power of the CUSUM test and the Wilcoxon change-point tests for a shift in the mean of a process with long-range dependent noise. We derive analytic formulas for the power of these tests under local alternatives. These results enable us to calculate the asymptotic relative efficiency (ARE) of the CUSUM test and the Wilcoxon change point test. We obtain the surprising result that for Gaussian data, the ARE of these two tests equals $1$, in contrast to the case of i.i.d. noise when the ARE is known to be $3/\pi$.

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Herold Dehling. Aeneas Rooch. Murad S. Taqqu. "Power of change-point tests for long-range dependent data." Electron. J. Statist. 11 (1) 2168 - 2198, 2017. https://doi.org/10.1214/17-EJS1283

Information

Received: 1 October 2014; Published: 2017
First available in Project Euclid: 19 May 2017

zbMATH: 1378.62064
MathSciNet: MR3654823
Digital Object Identifier: 10.1214/17-EJS1283

Subjects:
Primary: 60F17 , 62G30 , 62M10

Keywords: asymptotic relative efficiency of tests , long-range dependent data , Nonparametric change-point tests , power of test , Wilcoxon two-sample rank test

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Vol.11 • No. 1 • 2017
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