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Delay time in sequential detection of change

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  • Aue, Alexander
  • Horváth, Lajos

Abstract

We consider a sequential test procedure which detects possible changes in the mean of observations satisfying a weak invariance principle. Our test statistic is based on weighted CUSUMs of the underlying random variables. In this paper, we study the asymptotic behaviour of the delay time if a change has occurred in the sample after a training period of size m in which the observations stay in control. It turns out that in this situation the limiting distribution of the delay time for m-->[infinity] is normal under a suitable standardization provided the change appeared sufficiently soon after m.

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  • Aue, Alexander & Horváth, Lajos, 2004. "Delay time in sequential detection of change," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 221-231, April.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:3:p:221-231
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    1. Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
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    5. Lajos Horváth, 1997. "Detection of Changes in Linear Sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 271-283, June.
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    6. Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 2007. "On sequential detection of parameter changes in linear regression," Statistics & Probability Letters, Elsevier, vol. 77(9), pages 885-895, May.
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    8. Timmermann, Hella, 2015. "Sequential detection of gradual changes in the location of a general stochastic process," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 85-93.
    9. Alexander Aue & Lajos Horváth & Piotr Kokoszka & Josef Steinebach, 2008. "Monitoring shifts in mean: Asymptotic normality of stopping times," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 515-530, November.
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    11. KUROZUMI, Eiji & 黒住, 英司, 2016. "Monitoring Parameter Constancy with Endogenous Regressors," Discussion Papers 2016-01, Graduate School of Economics, Hitotsubashi University.
    12. Aue, Alexander & Horváth, Lajos & Reimherr, Matthew L., 2009. "Delay times of sequential procedures for multiple time series regression models," Journal of Econometrics, Elsevier, vol. 149(2), pages 174-190, April.
    13. Chen, Zhanshou & Tian, Zheng, 2010. "Modified procedures for change point monitoring in linear models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 62-75.
    14. Josef Steinebach, 2009. "Monitoring risk in a ruin model perturbed by diffusion," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(2), pages 205-224, September.
    15. Mihalache, Stefan, 2012. "Strong approximations and sequential change-point analysis for diffusion processes," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 464-472.
    16. Frisén, Marianne & Andersson, Eva & Schiöler, Linus, 2009. "Sufficient reduction in multivariate surveillance," Research Reports 2009:2, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    17. Josua Gösmann & Tobias Kley & Holger Dette, 2021. "A new approach for open‐end sequential change point monitoring," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(1), pages 63-84, January.
    18. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.
    19. Aue, Alexander, 2004. "Strong approximation for RCA(1) time series with applications," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 369-382, July.
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