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2020 Consistent nonparametric change point detection combining CUSUM and marked empirical processes
Maria Mohr, Natalie Neumeyer
Electron. J. Statist. 14(1): 2238-2271 (2020). DOI: 10.1214/20-EJS1715

Abstract

A weakly dependent time series regression model with multivariate covariates and univariate observations is considered, for which we develop a procedure to detect whether the nonparametric conditional mean function is stable in time against change point alternatives. Our proposal is based on a modified CUSUM type test procedure, which uses a sequential marked empirical process of residuals. We show weak convergence of the considered process to a centered Gaussian process under the null hypothesis of no change in the mean function and a stationarity assumption. This requires some sophisticated arguments for sequential empirical processes of weakly dependent variables. As a consequence we obtain convergence of Kolmogorov-Smirnov and Cramér-von Mises type test statistics. The proposed procedure acquires a very simple limiting distribution and nice consistency properties, features from which related tests are lacking. We moreover suggest a bootstrap version of the procedure and discuss its applicability in the case of unstable variances.

Citation

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Maria Mohr. Natalie Neumeyer. "Consistent nonparametric change point detection combining CUSUM and marked empirical processes." Electron. J. Statist. 14 (1) 2238 - 2271, 2020. https://doi.org/10.1214/20-EJS1715

Information

Received: 1 June 2019; Published: 2020
First available in Project Euclid: 3 June 2020

zbMATH: 07211000
MathSciNet: MR4106609
Digital Object Identifier: 10.1214/20-EJS1715

Subjects:
Primary: 62M10
Secondary: 62G08, 62G09, 62G10

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Vol.14 • No. 1 • 2020
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