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Confidence Intervals Based on Local Linear Smoother

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  • SONG XI CHEN
  • YONG SONG QIN

Abstract

Point‐wise confidence intervals for a non‐parametric regression function in conjunction with the popular local linear smoother are considered. The confidence intervals are based on the asymptotic normal distribution of the local linear smoother. Their coverage accuracy is evaluated by developing Edgeworth expansion for the coverage probability. It is found that the coverage error near the boundary of the support of the regression function is of a larger order than that in the interior, which implies that the local linear smoother is not adaptive to the boundary in terms of coverage. This is quite unexpected as the local linear smoother is adaptive to the boundary in terms of the mean squared error.

Suggested Citation

  • Song Xi Chen & Yong Song Qin, 2002. "Confidence Intervals Based on Local Linear Smoother," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 89-99, March.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:1:p:89-99
    DOI: 10.1111/1467-9469.00273
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    Cited by:

    1. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    2. Ke-Li Xu & Peter C. B. Phillips, 2011. "Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 518-528, October.
    3. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    4. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(2), pages 541-563, April.
    5. repec:cep:stiecm:/2014/573 is not listed on IDEAS
    6. Gery Geenens & Thomas Cuddihy, 2018. "Non‐parametric evidence of second‐leg home advantage in European football," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1009-1031, October.
    7. Peter C.B. Phillips & Ke-Li Xu, 2007. "Tilted Nonparametric Estimation of Volatility Functions," Cowles Foundation Discussion Papers 1612, Cowles Foundation for Research in Economics, Yale University, revised Jul 2010.
    8. K. De Brabanter & Y. Liu & C. Hua, 2016. "Convergence rates for uniform confidence intervals based on local polynomial regression estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 31-48, March.
    9. Pilar Olave & Eva Maria Andres & Jose Tomas Alcala, 2008. "Studying the relationship between unemployment periods in Spain: a nonparametric approach," Applied Economics Letters, Taylor & Francis Journals, vol. 15(9), pages 683-687.

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