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Uniform in Bandwidth Estimation of Integral Functionals of the Density Function

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  • EVARIST GINÉ
  • DAVID M. MASON

Abstract

. We apply recent results on local U‐statistics to obtain uniform in bandwidth consistency and central limit theorems for some commonly used estimators of integral functionals of density functions.

Suggested Citation

  • Evarist Giné & David M. Mason, 2008. "Uniform in Bandwidth Estimation of Integral Functionals of the Density Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 739-761, December.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:4:p:739-761
    DOI: 10.1111/j.1467-9469.2008.00600.x
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    References listed on IDEAS

    as
    1. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
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    Cited by:

    1. Mokkadem, Abdelkader & Pelletier, Mariane, 2020. "Online estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 166(C).
    2. Christopher Withers & Saralees Nadarajah, 2011. "Nonparametric confidence intervals for the integral of a function of an unknown density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 943-966.
    3. P. Patil & P. Patil & D. Bagkavos, 2012. "A measure of asymmetry," Statistical Papers, Springer, vol. 53(4), pages 971-985, November.
    4. José E. Chacón & Carlos Tenreiro, 2012. "Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 523-548, September.
    5. Chacón, José E. & Rodríguez-Casal, Alberto, 2010. "A note on the universal consistency of the kernel distribution function estimator," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1414-1419, September.
    6. Tiee-Jian Wu & Chih-Yuan Hsu & Huang-Yu Chen & Hui-Chun Yu, 2014. "Root $$n$$ n estimates of vectors of integrated density partial derivative functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 865-895, October.
    7. Christopher Partlett & Prakash Patil, 2017. "Measuring asymmetry and testing symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 429-460, April.

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