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Tie the straps: uniform bootstrap confidence bands for bounded influence curve estimators

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  • Wolfgang Karl Härdle
  • Ya'acov Ritov
  • Weining Wang

Abstract

We consider theoretical bootstrap \coupling" techniques for nonparametric robust smoothers and quantile regression, and verify the bootstrap improvement. To cope with curse of dimensionality, a variant of \coupling" bootstrap techniques are developed for additive models with both symmetric error distributions and further extension to the quantile regression framework. Our bootstrap method can be used in many situations like constructing con dence intervals and bands. We demonstrate the bootstrap improvement over the asymptotic band theoretically, and also in simulations and in applications to rm expenditures and the interaction of economic sectors and the stock market.

Suggested Citation

  • Wolfgang Karl Härdle & Ya'acov Ritov & Weining Wang, 2013. "Tie the straps: uniform bootstrap confidence bands for bounded influence curve estimators," SFB 649 Discussion Papers SFB649DP2013-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2013-047
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    References listed on IDEAS

    as
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    5. Horowitz, Joel L, 2001. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Econometrica, Econometric Society, vol. 69(2), pages 499-513, March.
    6. Wolfgang Karl Härdle & Ya’acov Ritov & Song Song, 2010. "Partial Linear Quantile Regression and Bootstrap Confidence Bands," SFB 649 Discussion Papers SFB649DP2010-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    More about this item

    Keywords

    Nonparametric Regression; Bootstrap; Quantile Regression; Con- dence Bands; Additive Model; Robust Statistics;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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