NP-Optimal Kernels for Nonparametric Sequential Detection Rules

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. ansgar.steland@ruhr-uni-bochum.de

Stochastics and Quality Control, 2003, vol. 18, issue 2, 149-163

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.

Keywords: Control charts; financial data; nonparametric regression; quality control; statistical genetics (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1515/EQC.2003.149

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