The Bernstein polynomial estimator of a smooth quantile function
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.
Volume (Year): 24 (1995)
Issue (Month): 4 (September)
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- 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.
- 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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