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A simple bootstrap method for constructing nonparametric confidence bands for functions

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  • Paul Hall
  • Joel Horowitz

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    (Institute for Fiscal Studies and Northwestern University)

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    Abstract

    Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches, and others based on nonstandard smoothing methods, complicate the process of inference, for example by requiring the choice of new, unconventional smoothing parameters and, in the case of undersmoothing, producing relatively wide bands. In this paper we suggest a new approach, which exploits to our advantage one of the difficulties that, in the past, has prevented an attractive solution to this problem - the fact that the standard bootstrap bias estimator suffers from relatively high-frequency stochastic error. The high frequency, together with a technique based on quantiles, can be exploited to dampen down the stochastic error term, leading to relatively narrow, simple-to-construct confidence bands.

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    File URL: http://www.cemmap.ac.uk/wps/cwp141212.pdf
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    Bibliographic Info

    Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP14/12.

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    Date of creation: Jun 2012
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    Handle: RePEc:ifs:cemmap:14/12

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    1. Hardle, W. & Marron, J., 1989. "Bootstrap Simultaneous Error Bars For Nonparametric Regression," CORE Discussion Papers 1989023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Tiejun Tong & Yuedong Wang, 2005. "Estimating residual variance in nonparametric regression using least squares," Biometrika, Biometrika Trust, vol. 92(4), pages 821-830, December.
    3. Hardle, W. & Huet, S. & Jolivet, E., 1991. "Better Bootstrap Confidence Intervals for Regression Curve Estimation," CORE Discussion Papers 1991056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Mendez, Guillermo & Lohr, Sharon, 2011. "Estimating residual variance in random forest regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2937-2950, November.
    5. Haerdle,Wolfgang & Bowman,Adrian, 1986. "Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands," Discussion Paper Serie A 71, University of Bonn, Germany.
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