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Tie the straps: Uniform bootstrap con fidence bands for bounded influence curve estimators

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

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 firm expenditures and the interaction of economic sectors and the stock market.

Suggested Citation

  • Härdle, Wolfgang Karl & Ritov, Ya'acov & Wang, Weining, 2013. "Tie the straps: Uniform bootstrap con fidence bands for bounded influence curve estimators," SFB 649 Discussion Papers 2013-047, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2013-047
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    References listed on IDEAS

    as
    1. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    2. Härdle, Wolfgang Karl & Ritov, Ya'acov & Song, Song, 2010. "Partial linear quantile regression and bootstrap confidence bands," SFB 649 Discussion Papers 2010-002, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
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    5. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1529-1564, October.
    6. 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.
    7. Härdle, Wolfgang K. & Song, Song, 2010. "Confidence Bands In Quantile Regression," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1180-1200, August.
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    More about this item

    Keywords

    Nonparametric Regression; Bootstrap; Quantile Regression; Confi 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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