The Bernstein polynomial estimator of a smooth quantile function
AbstractAn 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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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 24 (1995)
Issue (Month): 4 (September)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Kaigh, W. D. & Sorto, Maria Alejandra, 1993. "Subsampling quantile estimator majorization inequalities," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 373-379, December.
- 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.
- Zielinski, Ryszard, 1999. "Best equivariant nonparametric estimator of a quantile," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 79-84, October.
- 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.
- 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.
- 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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