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Almost-sure uniform error bounds of general smooth estimators of quantile density functions

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  • Cheng, Cheng

Abstract

Based on a careful analysis of the asymptotic almost-sure behavior of certain generalized Kiefer processes, asymptotic almost-sure uniform upper bounds of estimation error are established for a broad class of quantile density function estimators useful in survival analysis. The error bounds are given with explicit rate of convergence.

Suggested Citation

  • Cheng, Cheng, 2002. "Almost-sure uniform error bounds of general smooth estimators of quantile density functions," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 183-194, September.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:2:p:183-194
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    References listed on IDEAS

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    1. Aly, Emad-Eldin A. A. & Csörgo, Miklós & Horváth, Lajos, 1985. "Strong approximations of the quantile process of the product-limit estimator," Journal of Multivariate Analysis, Elsevier, vol. 16(2), pages 185-210, April.
    2. Falk, Michael, 1986. "On the estimation of the quantile density function," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 69-73, March.
    3. Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
    4. Kaigh, W. D. & Sorto, Maria Alejandra, 1993. "Subsampling quantile estimator majorization inequalities," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 373-379, December.
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    Cited by:

    1. P.G. Sankaran & N.N. Midhu, 2017. "Nonparametric estimation of mean residual quantile function under right censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(10), pages 1856-1874, July.
    2. 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.

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