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Local Linear Smoothers Using Asymmetric Kernels

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  • Song Chen

Abstract

This paper considers using asymmetric kernels in local linear smoothing to estimate a regression curve with bounded support. The asymmetric kernels are either beta kernels if the curve has a compact support or gamma kernels if the curve is bounded from one end only. While possessing the standard benefits of local linear smoothing, the local linear smoother using the beta or gamma kernel offers some extra advantages in aspects of having finite variance and resistance to sparse design. These are due to their flexible kernel shape and the support of the kernel matching the support of the regression curve.
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Suggested Citation

  • Song Chen, 2002. "Local Linear Smoothers Using Asymmetric Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 312-323, June.
    • Handle: RePEc:spr:aistmt:v:54:y:2002:i:2:p:312-323
    DOI: 10.1023/A:1022422002138
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    Cited by:

    1. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    2. Yuping Song & Hangyan Li & Yetong Fang, 2021. "Efficient estimation for the volatility of stochastic interest rate models," Statistical Papers, Springer, vol. 62(4), pages 1939-1964, August.
    3. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    4. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    5. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes," CIRJE F-Series CIRJE-F-573, CIRJE, Faculty of Economics, University of Tokyo.
    6. Eduardo Fé, 2010. "An application of local linear regression with asymmetric kernels to regression discontinuity designs," Economics Discussion Paper Series 1016, Economics, The University of Manchester.
    7. Funke, Benedikt & Hirukawa, Masayuki, 2021. "Bias correction for local linear regression estimation using asymmetric kernels via the skewing method," Econometrics and Statistics, Elsevier, vol. 20(C), pages 109-130.
    8. Masayuki Hirukawa & Irina Murtazashvili & Artem Prokhorov, 2022. "Uniform convergence rates for nonparametric estimators smoothed by the beta kernel," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1353-1382, September.

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