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A bootstrap method for constructing pointwise and uniform confidence bands for conditional quantile functions

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  • Joel L. Horowitz
  • Anand Krishnamurthy

Abstract

This paper is concerned with inference about the conditional quantile function in a nonparametric quantile regression model. Any method for constructing a confidence interval or band for this function must deal with the asymptotic bias of nonparametric estimators of the function. In estimation methods such as local polynomial estimation, this is usually done through undersmoothing or explicit bias correction. The latter usually requires oversmoothing. However, there are no satisfactory empirical methods for selecting bandwidths that under- or oversmooth. This paper extends the bootstrap method of Hall and Horowitz (2013) for conditional mean functions to conditional quantile functions. The paper also shows how the bootstrap method can be used to obtain uniform confidence bands. The bootstrap method uses only bandwidths that are selected by standard methods such as cross validation and plug-in. It does not use under- or oversmoothing. The results of Monte Carlo experiments illustrate the numerical performance of the bootstrap method.

Suggested Citation

  • Joel L. Horowitz & Anand Krishnamurthy, 2017. "A bootstrap method for constructing pointwise and uniform confidence bands for conditional quantile functions," CeMMAP working papers 01/17, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:01/17
    DOI: 10.1920/wp.cem.2017.0117
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    References listed on IDEAS

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    1. Song Xi Chen & Wolfgang Härdle & Ming Li, 2003. "An empirical likelihood goodness‐of‐fit test for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 663-678, August.
    2. Guerre, Emmanuel & Sabbah, Camille, 2012. "Uniform Bias Study And Bahadur Representation For Local Polynomial Estimators Of The Conditional Quantile Function," Econometric Theory, Cambridge University Press, vol. 28(1), pages 87-129, February.
    3. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004. "Bootstrap Inference In Semiparametric Generalized Additive Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 265-300, April.
    4. Y. Xia, 1998. "Bias‐corrected confidence bands in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 797-811.
    5. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. McMurry, Timothy L. & Politis, Dimitris N., 2008. "Bootstrap confidence intervals in nonparametric regression with built-in bias correction," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2463-2469, October.
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