Open Access
2017 Change point estimation based on Wilcoxon tests in the presence of long-range dependence
Annika Betken
Electron. J. Statist. 11(2): 3633-3672 (2017). DOI: 10.1214/17-EJS1323


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.


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Annika Betken. "Change point estimation based on Wilcoxon tests in the presence of long-range dependence." Electron. J. Statist. 11 (2) 3633 - 3672, 2017.


Received: 1 January 2017; Published: 2017
First available in Project Euclid: 6 October 2017

zbMATH: 1373.62123
MathSciNet: MR3709865
Digital Object Identifier: 10.1214/17-EJS1323

Primary: 62G05 , 62M10
Secondary: 60G15 , 60G22

Keywords: change point estimation , long-range dependence , self-normalization , Wilcoxon test

Vol.11 • No. 2 • 2017
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