The Bernstein polynomial estimator of a smooth quantile function

DOI10.1016/0167-7152(94)00190-JzbMath0835.62036MaRDI QIDQ1903180

Cheng Cheng

Publication date: 23 April 1996

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

uniform approximationspectral decompositionoscillation behaviorweighted Brownian bridgeempirical quantile functionsmooth quantile functionBernstein polynomial smoothingpreservation of high-order convexity

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Order statistics; empirical distribution functions (62G30)

Related Items

RATIONAL SPLINE ESTIMATORS OF THE QUANTILE FUNCTION, Bayesian density estimation using bernstein polynomials, Unified estimators of smooth quantile and quantile density functions, Uniform consistency of generalized kernel estimators of quantile density, New approaches to nonparametric density estimation and selection of smoothing parameters, Estimation of the quantile function using Bernstein–Durrmeyer polynomials, A note on generalized Bernstein polynomial density estimators, Asymptotic distribution and simultaneous confidence bands for ratios of quantile functions, Sharp distribution-free bounds on the bias in estimating quantiles via order statistics, Bayesian bridge-randomized penalized quantile regression, Parametric modeling of quantile regression coefficient functions, Best equivariant nonparametric estimator of a quantile, Asymptotic properties of Bernstein estimators on the simplex, A Berry-Esseen-type theorem of quantile density estimators, Quantile estimation via distribution fitting, Estimation of probability characteristics by generalized Bernstein polynomials, Small-Sample Quantile Estimators in a Large Nonparametric Model, Almost-sure uniform error bounds of general smooth estimators of quantile density functions.

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