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NP-Optimal Kernels for Nonparametric Sequential Detection Rules

NP-Optimal Kernels for Nonparametric Sequential Detection Rules 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

NP-Optimal Kernels for Nonparametric Sequential Detection Rules

Economic Quality Control , Volume 18 (2) – Oct 1, 2003

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Publisher
de Gruyter
Copyright
Copyright © 2003 by the
ISSN
1869-6147
eISSN
1869-6147
DOI
10.1515/EQC.2003.149
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Economic Quality Controlde Gruyter

Published: Oct 1, 2003

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