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NP-optimal kernels for nonparametric sequential detection rules

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  • Steland, Ansgar

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, 2004. "NP-optimal kernels for nonparametric sequential detection rules," Technical Reports 2004,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200409
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    References listed on IDEAS

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    1. Steland, Ansgar, 2003. "Sequential control of time series by functionals of kernel-weighted empirical processes under local alternatives," Technical Reports 2003,19, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. 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.
    3. GIOT, Pierre, 1999. "Time transformations, intraday data and volatility models," LIDAM Discussion Papers CORE 1999044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Steland Ansgar, 2002. "A Bayesian View on Detecting Drifts by Nonparametric Methods," Stochastics and Quality Control, De Gruyter, vol. 17(2), pages 177-186, January.
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