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A Bayesian View on Detecting Drifts by Nonparametric Methods

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  • Steland Ansgar

    (Ruhr-Universität Bochum, Fakultät für Mathematik, Mathematik 3 NA 3/71, Universitätsstr. 150, D-44780 Bochum, Germany)

Abstract

We study a nonparametric sequential detection procedure, which aims at detecting the first time point where a drift term appears in a stationary process, from a Bayesian perspective. The approach is based on a nonparametric model for the drift, a nonparametric kernel smoother which is used to define the stopping rule, and a performance measure which determines for each smoothing kernel and each given drift the asymptotic accuracy of the method. We look at this approach by parameterizing the drift and putting a prior distribution on the parameter vector. We are able to identify the optimal prior distribution which minimizes the expected performance measure. Consequently, we can judge whether a certain prior distribution yields good or even optimal asymptotic detection. We consider several important special cases where the optimal prior can be calculated explicitly.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:ecqcon:v:17:y:2002:i:2:p:177-186:n:4
    DOI: 10.1515/EQC.2002.177
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    Cited by:

    1. Steland, Ansgar, 2004. "NP-optimal kernels for nonparametric sequential detection rules," Technical Reports 2004,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. 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.
    3. Steland, Ansgar, 2004. "Random walks with drift : a sequential approach," Technical Reports 2004,50, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Steland, Ansgar, 2003. "Optimal sequential kernel detection for dependent processes," Technical Reports 2003,27, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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