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Optimal sequential kernel detection for dependent processes

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  • Steland, Ansgar

Abstract

In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential nonparametric kernel procedures under local nonparametric alternatives. We prove a new theorem on the convergence of the normed delay of the associated sequential detection procedure which holds for dependent time series under a weak mixing condition. The result suggests a simple procedure to select a kernel from a finite set of candidate kernels, and therefore may also be of interest from a practical point of view. Further, we provide two new theorems about the existence and an explicit representation of optimal kernels minimizing the asymptotic normed delay. The results are illustrated by some examples.

Suggested Citation

  • Steland, Ansgar, 2003. "Optimal sequential kernel detection for dependent processes," Technical Reports 2003,27, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  • Handle: RePEc:zbw:sfb475:200327
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    References listed on IDEAS

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    1. Marianne Frisén, 2003. "Statistical Surveillance. Optimality and Methods," International Statistical Review, International Statistical Institute, vol. 71(2), pages 403-434, August.
    2. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    3. 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.
    4. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
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