Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 11, Number 2 (2017), 3633-3672.
Change point estimation based on Wilcoxon tests in the presence of long-range dependence
We consider an estimator for the location of a shift in the mean of long-range dependent sequences. The estimation is based on the two-sample Wilcoxon statistic. Consistency and the rate of convergence for the estimated change point are established. In the case of a constant shift height, the $1/n$ convergence rate (with $n$ denoting the number of observations), which is typical under the assumption of independent observations, is also achieved for long memory sequences. It is proved that if the change point height decreases to $0$ with a certain rate, the suitably standardized estimator converges in distribution to a functional of a fractional Brownian motion. The estimator is tested on two well-known data sets. Finite sample behaviors are investigated in a Monte Carlo simulation study.
Electron. J. Statist., Volume 11, Number 2 (2017), 3633-3672.
Received: January 2017
First available in Project Euclid: 6 October 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G05: Estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G15: Gaussian processes 60G22: Fractional processes, including fractional Brownian motion
Betken, Annika. Change point estimation based on Wilcoxon tests in the presence of long-range dependence. Electron. J. Statist. 11 (2017), no. 2, 3633--3672. doi:10.1214/17-EJS1323. https://projecteuclid.org/euclid.ejs/1507255616