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Nonparametric estimation of a quantile density function by wavelet methods

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  • Chesneau, Christophe
  • Dewan, Isha
  • Doosti, Hassan

Abstract

In this paper nonparametric wavelet estimators of the quantile density function are proposed. Consistency of the wavelet estimators is established under the Lp risk. A simulation study illustrates the good performance of our estimators.

Suggested Citation

  • Chesneau, Christophe & Dewan, Isha & Doosti, Hassan, 2016. "Nonparametric estimation of a quantile density function by wavelet methods," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 161-174.
    • Handle: RePEc:eee:csdana:v:94:y:2016:i:c:p:161-174
    DOI: 10.1016/j.csda.2015.08.006
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    References listed on IDEAS

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    1. M. Jones, 1992. "Estimating densities, quantiles, quantile densities and density quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(4), pages 721-727, December.
    2. Sankaran, P.G. & Unnikrishnan Nair, N. & Sreedevi, E.P., 2010. "A quantile based test for comparing cumulative incidence functions of competing risks models," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 886-891, May.
    3. Gaëlle Chagny & Claire Lacour, 2015. "Optimal adaptive estimation of the relative density," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 605-631, September.
    4. L. Peng & J. P. Fine, 2007. "Nonparametric quantile inference with competing–risks data," Biometrika, Biometrika Trust, vol. 94(3), pages 735-744.
    5. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    6. Christophe Chesneau & Isha Dewan & Hassan Doosti, 2012. "Wavelet linear density estimation for associated stratified size-biased sample," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 429-445.
    7. Abbaszadeh, Mohammad & Chesneau, Christophe & Doosti, Hassan, 2012. "Nonparametric estimation of density under bias and multiplicative censoring via wavelet methods," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 932-941.
    8. Soni, Pooja & Dewan, Isha & Jain, Kanchan, 2012. "Nonparametric estimation of quantile density function," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3876-3886.
    9. P. Sankaran & N. Unnikrishnan Nair, 2009. "Nonparametric estimation of hazard quantile function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(6), pages 757-767.
    10. Soni, Pooja & Dewan, Isha & Jain, Kanchan, 2015. "Tests for successive differences of quantiles," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 1-8.
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    Cited by:

    1. Federico Palacios-González & Rosa M. García-Fernández, 2020. "A faster algorithm to estimate multiresolution densities," Computational Statistics, Springer, vol. 35(3), pages 1207-1230, September.
    2. Fabian Dunker & Stephan Klasen & Tatyana Krivobokova, 2017. "Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions," Papers 1710.09009, arXiv.org.
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