Weighted uniform consistency of kernel density estimators.

DOI10.1214/009117904000000063zbMath1052.62034arXivmath/0410170OpenAlexW2016095499MaRDI QIDQ1889792

Joel Zinn, Evarist Giné M., Vladimir I. Koltchinskii

Publication date: 10 December 2004

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

Full work available at URL: https://arxiv.org/abs/math/0410170

zbMATH Keywords

rates of convergenceKernel density estimatorweak and strong weighted uniform consistencyweighted \(L_\infty\)-norm

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Strong limit theorems (60F15)

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Cites Work

• U-processes: Rates of convergence
• The oscillation behavior of empirical processes: The multivariate case
• Some limit theorems for empirical processes (with discussion)
• Laws of the iterated logarithm in the tails for weighted uniform empirical processes
• Strong limit theorems for weighted quantile processes
• A law of the logarithm for kernel density estimators
• Weak and strong uniform consistency of the kernel estimate of a density and its derivatives
• Sharper bounds for Gaussian and empirical processes
• Rates of strong uniform consistency for multivariate kernel density estimators. (Vitesse de convergence uniforme presque sûre pour des estimateurs à noyaux de densités multivariées)
• A uniform functional law of the logarithm for the local empirical process.
• Bounds for weighted multivariate empirical distribution functions
• Remarks on Some Nonparametric Estimates of a Density Function
• Uniform Central Limit Theorems
• On Estimation of a Probability Density Function and Mode
• Convergence of stochastic processes
• An empirical process approach to the uniform consistency of kernel-type function estimators
• On consistency of kernel density estimators for randomly censored data: Rates holding uniformly over adaptive intervals
• New concentration inequalities in product spaces
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