Abstract
Bootstrap methods for sequential change-point detection procedures in linear regression models are proposed. The corresponding monitoring procedures are designed to control the overall significance level. The bootstrap critical values are updated constantly by including new observations obtained from the monitoring. The theoretical properties of these sequential bootstrap procedures are investigated, showing their asymptotic validity. Bootstrap and asymptotic methods are compared in a simulation study, showing that the studentized bootstrap tests hold the overall level better especially for small historic sample sizes while having a comparable power and run length.
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The work was supported by DFG-Grant KI 1443/2-1, the work of the first author was supported by MSM 0021620839 and GACR 201/09/J006 and the position of the second author was financed by the Stifterverband für die Deutsche Wissenschaft by funds of the Claussen-Simon-trust.
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Hušková, M., Kirch, C. Bootstrapping sequential change-point tests for linear regression. Metrika 75, 673–708 (2012). https://doi.org/10.1007/s00184-011-0347-7
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DOI: https://doi.org/10.1007/s00184-011-0347-7