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A New Kernel Distribution Function Estimator Based on a Non‐parametric Transformation of the Data

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  • JAN W. H. SWANEPOEL
  • FRANCOIS C. VAN GRAAN

Abstract

. A new kernel distribution function (df) estimator based on a non‐parametric transformation of the data is proposed. It is shown that the asymptotic bias and mean squared error of the estimator are considerably smaller than that of the standard kernel df estimator. For the practical implementation of the new estimator a data‐based choice of the bandwidth is proposed. Two possible areas of application are the non‐parametric smoothed bootstrap and survival analysis. In the latter case new estimators for the survival function and the mean residual life function are derived.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:4:p:551-562
    DOI: 10.1111/j.1467-9469.2005.00472.x
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    Citations

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    Cited by:

    1. Catalina Bolancé & Montserrat Guillen, 2021. "Nonparametric Estimation of Extreme Quantiles with an Application to Longevity Risk," Risks, MDPI, vol. 9(4), pages 1-23, April.
    2. Steven Abrams & Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2020. "Nonparametric estimation of the cross ratio function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 771-801, June.
    3. David Mason & Jan Swanepoel, 2011. "A general result on the uniform in bandwidth consistency of kernel-type function estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 72-94, May.
    4. Suparna Biswas & Rituparna Sen, 2019. "Kernel Based Estimation of Spectral Risk Measures," Papers 1903.03304, arXiv.org, revised Dec 2023.
    5. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 255-262.
    6. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    7. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers 2014-05, Universitat de Barcelona, UB Riskcenter.
    8. Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.
    9. Arup Bose & Santanu Dutta, 2022. "Kernel based estimation of the distribution function for length biased data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 269-287, April.
    10. 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.
    11. D. Blanke & D. Bosq, 2018. "Polygonal smoothing of the empirical distribution function," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 263-287, July.

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