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The Bernstein polynomial estimator of a smooth quantile function

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  • Cheng, Cheng
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-3YCN1N9-6/2/d61b019c3e38d33d2b2999f0e3b79359
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 24 (1995)
    Issue (Month): 4 (September)
    Pages: 321-330

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    Handle: RePEc:eee:stapro:v:24:y:1995:i:4:p:321-330

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    Related research

    Keywords: Quantile function Bernstein polynomial Smoothing Approximation Spectral decomposition Convexity;

    References

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    1. Kaigh, W. D. & Sorto, Maria Alejandra, 1993. "Subsampling quantile estimator majorization inequalities," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 373-379, December.
    2. 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.
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    Cited by:
    1. Zielinski, Ryszard, 1999. "Best equivariant nonparametric estimator of a quantile," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 79-84, October.
    2. 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.
    3. 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.
    4. 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.

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