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Fourier methods for smooth distribution function estimation

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  • Chacón, José E.
  • Monfort, Pablo
  • Tenreiro, Carlos

Abstract

The limit behavior of the optimal bandwidth sequence for the kernel distribution function estimator is analyzed, in its greatest generality, by using Fourier transform methods. We show a class of distributions for which the kernel estimator achieves a first-order improvement in efficiency over the empirical estimator.

Suggested Citation

  • Chacón, José E. & Monfort, Pablo & Tenreiro, Carlos, 2014. "Fourier methods for smooth distribution function estimation," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 223-230.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:223-230
    DOI: 10.1016/j.spl.2013.10.010
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    References listed on IDEAS

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    1. Jan W. H. Swanepoel & Francois C. Van Graan, 2005. "A New Kernel Distribution Function Estimator Based on a Non‐parametric Transformation of the Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 551-562, December.
    2. Jones, M. C., 1990. "The performance of kernel density functions in kernel distribution function estimation," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 129-132, February.
    3. Ingrid K. Glad & Nils Lid Hjort & Nikolai G. Ushakov, 2003. "Correction of Density Estimators that are not Densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 415-427, June.
    4. Shao, Yongzhao & Xiang, Xiaojing, 1997. "Some extensions of the asymptotics of a kernel estimator of a distribution function," Statistics & Probability Letters, Elsevier, vol. 34(3), pages 301-308, June.
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