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Large sample results for varying kernel regression estimates

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  • Hira L. Koul
  • Weixing Song

Abstract

The varying kernel density estimates are particularly designed for positive random variables. Unlike the commonly used symmetric kernel density estimates, the varying kernel density estimates do not suffer from the boundary problem. This paper establishes asymptotic normality and uniform almost sure convergence results for a varying kernel density estimate when the underlying random variable is positive. Similar results are also obtained for a varying kernel nonparametric estimate of the regression function when the covariate is positive. Pros and cons of the varying kernel regression estimate are also discussed via a simulation study.

Suggested Citation

  • Hira L. Koul & Weixing Song, 2013. "Large sample results for varying kernel regression estimates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 829-853, December.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:829-853
    DOI: 10.1080/10485252.2013.810742
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    Citations

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    Cited by:

    1. Xu Li & Juxia Xiao & Weixing Song & Jianhong Shi, 2019. "Local linear regression with reciprocal inverse Gaussian kernel," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 733-758, August.
    2. Juxia Xiao & Xu Li & Jianhong Shi, 2019. "Local linear smoothers using inverse Gaussian regression," Statistical Papers, Springer, vol. 60(4), pages 1225-1253, August.
    3. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    4. 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.
    5. N. Balakrishna & Hira L. Koul, 2017. "Varying kernel marginal density estimator for a positive time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 531-552, July.
    6. Gaku Igarashi, 2018. "Multivariate Density Estimation Using a Multivariate Weighted Log-Normal Kernel," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 247-266, August.
    7. Kakizawa, Yoshihide, 2022. "Multivariate elliptical-based Birnbaum–Saunders kernel density estimation for nonnegative data," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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