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NP-Optimal Kernels for Nonparametric Sequential Detection Rules

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  • Steland Ansgar

    (Ruhr-Universität Bochum, Fakultät für Mathematik, Mathematik 3 NA 3/71, Universitätsstr. 150, D-44780 Bochum, Germany. ansgar.steland@ruhr-uni-bochum.de)

Abstract

An attractive nonparametric method to detect change-points sequentially is to apply control charts based on kernel smoothers. Recently, the strong convergence of the associated normed delay associated with such a sequential stopping rule has been studied under sequences of out-of-control models. Kernel smoothers employ a kernel function to downweight past data. Since kernel functions with values in the unit interval are sufficient for that task, we study the problem to optimize the asymptotic normed delay over a class of kernels ensuring that restriction and certain additional moment constraints. We apply the key theorem to discuss several important examples where explicit solutions exist to illustrate that the results are applicable.

Suggested Citation

  • Steland Ansgar, 2003. "NP-Optimal Kernels for Nonparametric Sequential Detection Rules," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 149-163, January.
    • Handle: RePEc:bpj:ecqcon:v:18:y:2003:i:2:p:149-163:n:1
    DOI: 10.1515/EQC.2003.149
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    References listed on IDEAS

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    1. Pawlak, Mirek & Rafajlowicz, Ewaryst & Steland, Ansgar, 2003. "On detecting jumps in time series: Nonparametric setting," Technical Reports 2003,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Dietmar Ferger, 1994. "On the power of nonparametric changepoint-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 277-292, December.
    3. Ferger, D., 1994. "An Extension of the Csörgo-Horváth Functional Limit Theorem and Its Applications to Changepoint Problems," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 338-351, November.
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