Electronic Journal of Statistics

Power of change-point tests for long-range dependent data

Herold Dehling, Aeneas Rooch, and Murad S. Taqqu

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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 $3/\pi$.

Article information

Electron. J. Statist., Volume 11, Number 1 (2017), 2168-2198.

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

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Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62G30: Order statistics; empirical distribution functions 60F17: Functional limit theorems; invariance principles

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

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Dehling, Herold; Rooch, Aeneas; Taqqu, Murad S. Power of change-point tests for long-range dependent data. Electron. J. Statist. 11 (2017), no. 1, 2168--2198. doi:10.1214/17-EJS1283. https://projecteuclid.org/euclid.ejs/1495159237

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