Uniform consistency of generalized kernel estimators of quantile density

DOI10.1214/aos/1034713657zbMath0853.62031OpenAlexW2086756049MaRDI QIDQ1922390

Cheng Cheng

Publication date: 1 September 1996

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1034713657

zbMATH Keywords

approximationsmoothing methodsquantile density estimationgeneralized kernel smoothingsmoothed Brownian bridgesuniform in-probability consistency

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20)

Related Items (13)

New methods for bias correction at endpoints and boundaries ⋮ Weighted least squares estimators for the Parzen tail index ⋮ Nonparametric C- and D-vine-based quantile regression ⋮ New kernel-type estimator of Shanonn's entropy ⋮ Concentration order on a metric space, with some statistical applications ⋮ Asymptotic distribution and simultaneous confidence bands for ratios of quantile functions ⋮ Tail exponent estimation via broadband log density-quantile regression ⋮ On some smooth estimators of the quantile function for a stationary associated process ⋮ Hermite expansion and estimation of monotonic transformations of Gaussian data ⋮ A Berry-Esseen-type theorem of quantile density estimators ⋮ New Entropy Estimator with an Application to Test of Normality ⋮ Some Nonparametric Tests for Change-Point Detection Based on the ℙ-ℙ and ℚ-ℚ Plot Processes ⋮ Almost-sure uniform error bounds of general smooth estimators of quantile density functions.

Cites Work

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• Strong laws for density estimators of Bernstein type
• On the estimation of the quantile density function
• Kernel approximations of a Wiener process
• Strong approximations of the quantile process
• A law of the logarithm for kernel quantile density estimators
• The Bernstein polynomial estimator of a smooth quantile function
• Distribution of quantiles in samples from a bivariate population
• Subsampling quantile estimators and uniformity criteria
• ESTIMATION OF A DENSITY FUNCTION USING ORDER STATISTICS1
• Nonparametric Statistical Data Modeling
• On Monosplines of Least Deviation and Best Quadrature Formulae
• On a Simple Estimate of the Reciprocal of the Density Function

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