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Density estimates of low bias

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  • Christopher Withers
  • Saralees Nadarajah

Abstract

Two methods are given for adapting a kernel density estimate to obtain an estimate of a density function with bias O(h p ) for any given p, where h=h(n) is the bandwidth and n is the sample size. The first method is standard. The second method is new and involves use of Bell polynomials. The second method is shown to yield smaller biases and smaller mean squared errors than classical kernel density estimates and those due to Jones et al. (Biometrika 82:327–338, 1995 ). Copyright Springer-Verlag 2013

Suggested Citation

  • Christopher Withers & Saralees Nadarajah, 2013. "Density estimates of low bias," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 357-379, April.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:3:p:357-379
    DOI: 10.1007/s00184-012-0392-x
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    References listed on IDEAS

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    1. Kairat Mynbaev & Carlos Martins-Filho, 2010. "Bias reduction in kernel density estimation via Lipschitz condition," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 219-235.
    2. 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.
    3. Stephan R. Sain & David W. Scott, 2002. "Zero‐Bias Locally Adaptive Density Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 441-460, September.
    4. Hazelton, Martin L. & Turlach, Berwin A., 2007. "Reweighted kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3057-3069, March.
    5. Hazelton, Martin L., 1998. "Bias annihilating bandwidths for kernel density estimation at a point," Statistics & Probability Letters, Elsevier, vol. 38(4), pages 305-309, July.
    6. Peter Hall & Michael C. Minnotte, 2002. "High order data sharpening for density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 141-157, January.
    7. Yoshihiko Nishiyama & Peter M. Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 73(3), pages 903-948, May.
    8. Marco Di Marzio, 2004. "Boosting kernel density estimates: A bias reduction technique?," Biometrika, Biometrika Trust, vol. 91(1), pages 226-233, March.
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    1. Mynbaev, Kairat T. & Nadarajah, Saralees & Withers, Christopher S. & Aipenova, Aziza S., 2014. "Improving bias in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 106-112.

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