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Sequential control of time series by functionals of kernal-weighted empirical processes under local alternatives

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  • Ansgar Steland

Abstract

Motivated in part by applications in model selection in statistical genetics and sequential monitoring of financial data, we study an empirical process framework for a class of stopping rules which rely on kernel-weighted averages of past data. We are interested in the asymptotic distribution for time series data and an analysis of the joint influence of the smoothing policy and the alternative defining the deviation from the null model (in-control state). We employ a certain type of local alternative which provides meaningful insights. Our results hold true for short memory processes which satisfy a weak mixing condition. By relying on an empirical process framework we obtain both asymptotic laws for the classical fixed sample design and the sequential monitoring design. As a by-product we establish the asymptotic distribution of the Nadaraya-Watson kernel smoother when the regressors do not get dense as the sample size increases. Copyright Springer-Verlag 2004

Suggested Citation

  • Ansgar Steland, 2004. "Sequential control of time series by functionals of kernal-weighted empirical processes under local alternatives," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(3), pages 229-249, November.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:3:p:229-249
    DOI: 10.1007/s001840300306
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    Cited by:

    1. Steland, Ansgar, 2005. "On the distribution of the clipping median under a mixture model," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 1-13, January.
    2. Ansgar Steland, 2005. "Random Walks with Drift – A Sequential Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 917-942, November.
    3. Steland, Ansgar, 2006. "A bootstrap view on dickey-fuller control charts for AR(1) series," Technical Reports 2006,01, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Steland, Ansgar, 2005. "On detection of unit roots generalizing the classic Dickey-Fuller approach," Technical Reports 2005,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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