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2021 Sequential change point test in the presence of outliers: the density power divergence based approach
Junmo Song
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Electron. J. Statist. 15(1): 3504-3550 (2021). DOI: 10.1214/21-EJS1868

Abstract

In this study, we consider a problem of monitoring parameter changes particularly in the presence of outliers. To propose a sequential procedure that is robust against outliers, we use the density power divergence to derive a detector and stopping time that make up our procedure. We first investigate the asymptotic properties of our sequential procedure for i.i.d. sequences and then extend the proposed procedure to stationary time series models, where we provide a set of sufficient conditions under which the proposed procedure has an asymptotically controlled size and consistency in power. As an application, our procedure is applied to the GARCH models. We demonstrate the validity and robustness of the proposed procedure through a simulation study. Finally, two real data analyses are provided to illustrate the usefulness of the proposed sequential procedure.

Funding Statement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01056924).

Acknowledgments

The author would like to thank the associate editor for carefully examining the paper and providing valuable comments.

Citation

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Junmo Song. "Sequential change point test in the presence of outliers: the density power divergence based approach." Electron. J. Statist. 15 (1) 3504 - 3550, 2021. https://doi.org/10.1214/21-EJS1868

Information

Received: 1 December 2020; Published: 2021
First available in Project Euclid: 7 July 2021

arXiv: 2008.02365
Digital Object Identifier: 10.1214/21-EJS1868

Subjects:
Primary: 62F35, 62L10
Secondary: 62M10

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Vol.15 • No. 1 • 2021
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