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The Bernstein polynomial estimator of a smooth quantile function

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  • Cheng, Cheng

Abstract

An estimator of a smooth quantile function (q.f.) is constructed by Bernstein polynomial smoothing of the empirical quantile function. Asymptotic behavior of this estimator is demonstrated by a weighted Brownian bridge in-probability uniform approximation. Oscillation behavior of this estimator in finite samples is demonstrated by spectral decomposition and preservation of high-order convexity of the empirical quantile function.

Suggested Citation

  • Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
  • Handle: RePEc:eee:stapro:v:24:y:1995:i:4:p:321-330
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    References listed on IDEAS

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    1. Munoz Perez, Jose & Fernandez Palacin, Ana, 1987. "Estimating the quantile function by Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 391-397, September.
    2. 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. Cheng, Cheng, 1998. "A Berry-Esséen-type theorem of quantile density estimators," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 255-262, August.
    2. Okolewski, Andrzej & Rychlik, Tomasz, 2001. "Sharp distribution-free bounds on the bias in estimating quantiles via order statistics," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 207-213, April.
    3. Zielinski, Ryszard, 1999. "Best equivariant nonparametric estimator of a quantile," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 79-84, October.
    4. Golyandina, Nina & Pepelyshev, Andrey & Steland, Ansgar, 2012. "New approaches to nonparametric density estimation and selection of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2206-2218.
    5. 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.

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