A Bayesian View on Detecting Drifts by Nonparametric Methods

Steland Ansgar
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Steland Ansgar: Ruhr-Universität Bochum, Fakultät für Mathematik, Mathematik 3 NA 3/71, Universitätsstr. 150, D-44780 Bochum, Germany

Stochastics and Quality Control, 2002, vol. 17, issue 2, 177-186

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.

Keywords: Bayesian robustness; control chart; economic control; jump-preserving estimation; quality control; sequential analysis (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (4)

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DOI: 10.1515/EQC.2002.177

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