Asymptotic theorems for kernel U-quantiles

DOI10.1214/12-EJS687zbMath1276.62028MaRDI QIDQ1950833

Stefan S. Ralescu

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ejs/1334754010

zbMATH Keywords

Bahadur representationinvariance principleskernel estimator

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Cites Work

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• Bahadur representation for \(U\)-quantiles of dependent data
• Relative deficiency of kernel type estimators of quantiles
• Generalized L-, M-, and R-statistics
• Asymptotic normality of the kernel quantile estimator
• The almost sure invariance principle for the empirical process of U- statistic structure
• A kernel-type estimator for generalized quantiles
• Generalized order statistics, Bahadur representations, and sequential nonparametric fixed-width confidence intervals
• The Bahadur-Kiefer representation for \(U\)-quantiles
• Strong approximation theorems for integrated kernel quantiles
• Kernel Quantile Estimators
• A Smooth Nonparametric Estimator of a Quantile Function
• Nonparametric Statistical Data Modeling
• Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions