Asymptotics of Suprema of Weighted Gaussian Fields with Applications to Kernel Density Estimators

DOI10.1137/S0040585X97T987211zbMath1344.60052OpenAlexW1255655378MaRDI QIDQ2944445

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Publication date: 2 September 2015

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97t987211

zbMATH Keywords

Gaussian processeskernel density estimatorsweighted sup-normlocal invariance principle

Mathematics Subject Classification ID

Random fields (60G60) Density estimation (62G07) Gaussian processes (60G15) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05)

Related Items (2)

On sufficient conditions for a Gaussian approximation of kernel estimates for distribution densities ⋮ A review of uncertainty quantification for density estimation

Cites Work

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• On the convergence rate of maximal deviation distribution for kernel regression estimates
• Local invariance principles and their application to density estimation
• Kernel density estimators: convergence in distribution for weighted sup-norms
• Weighted uniform consistency of kernel density estimators.
• Weak convergence and empirical processes. With applications to statistics
• On some global measures of the deviations of density function estimates
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Upcrossing Probabilities for Stationary Gaussian Processes

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