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Confidence intervals for nonparametric regression

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  • Lawrence Brown
  • Xin Fu
  • Linda Zhao

Abstract

In nonparametric function estimation, providing a confidence interval with the right coverage is a challenging problem. This is especially the case when the underlying function has a wide range of unknown degrees of smoothness. Here, we propose two methods of constructing an average coverage confidence interval built from block shrinkage estimation methods. One is based on the James–Stein shrinkage estimator; the other begins with a Bayesian perspective and is based on a modification of the harmonic prior estimator. Simulation shows that these confidence intervals have average coverage close to or above the nominal coverage even when the underlying function is rough and/or the signal-to-noise ratio is small. Both of the confidence intervals perform consistently well across all the investigated test functions even though these functions have very different shapes and smoothness.

Suggested Citation

  • Lawrence Brown & Xin Fu & Linda Zhao, 2011. "Confidence intervals for nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 149-163.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:149-163
    DOI: 10.1080/10485251003753201
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    References listed on IDEAS

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    1. Wenxin Mao & Linda H. Zhao, 2003. "Free‐knot polynomial splines with confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 901-919, November.
    2. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    3. Stuart Barber & Guy P. Nason & Bernard W. Silverman, 2002. "Posterior probability intervals for wavelet thresholding," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 189-205, May.
    4. Hardle, W. & Marron, J., 1989. "Bootstrap Simultaneous Error Bars For Nonparametric Regression," LIDAM Discussion Papers CORE 1989023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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