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Smoothed influence function: Another view at robust nonparametric regression

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  • Tamine, Julien

Abstract

In this work, we introduce a smoothed influence function that constitute a theoretical tool for studying the outliers robustness properties of a large class of nonparametric estimators. With this tool, we first show the nonrobustness of the Nadaraya-Watson estimator of regression. Then we show that the M, the L and the R-estimators of the regression achieve robustness (when estimated by kernel). Our results are illustrated performing Monte-Carlo simulation.

Suggested Citation

  • Tamine, Julien, 2001. "Smoothed influence function: Another view at robust nonparametric regression," SFB 373 Discussion Papers 2002,62, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200262
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    References listed on IDEAS

    as
    1. Klinke, Sigbert & Witzel, Rodrigo, 2002. "MD*Book online: A tool for creating interactive documents," SFB 373 Discussion Papers 2002,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Wolfgang Härdle & Torsten Kleinow & Rolf Tschernig, 2001. "Web Quantlets for Time Series Analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, pages 179-188.
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    More about this item

    Keywords

    robustness; nonparametric regression; influence function; M-estimator; L-estimator; R-estimator; Von-mises statistical functional generalized Delta-theorem;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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