## Electronic Journal of Statistics

### Change point estimation based on Wilcoxon tests in the presence of long-range dependence

Annika Betken

#### Abstract

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.

#### Article information

Source
Electron. J. Statist., Volume 11, Number 2 (2017), 3633-3672.

Dates
First available in Project Euclid: 6 October 2017

https://projecteuclid.org/euclid.ejs/1507255616

Digital Object Identifier
doi:10.1214/17-EJS1323

Mathematical Reviews number (MathSciNet)
MR3709865

Zentralblatt MATH identifier
1373.62123

#### Citation

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

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