Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 11, Number 1 (2017), 2168-2198.
Power of change-point tests for long-range dependent data
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 $3/\pi$.
Electron. J. Statist., Volume 11, Number 1 (2017), 2168-2198.
Received: October 2014
First available in Project Euclid: 19 May 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62G30: Order statistics; empirical distribution functions 60F17: Functional limit theorems; invariance principles
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