Rate of strong uniform convergence of k-NN density estimates
type: Item
instance of: scholarly article
title: Rate of strong uniform convergence of k-NN density estimates
zbMATH Open document ID: 0536.62032
DOI: 10.1016/0378-3758(83)90037-X
author: Y. P. Mack
published in: Journal of Statistical Planning and Inference
publication date: 1983-01-01T00:00:00Z
review text: The author uses recent results of \textit{W. Stute} [Ann. Probab. 10, 86-107 and 414-422 (1982; Zbl 0489.60038 and Zbl 0493.62040, respectively)] on the oscillation behavior of empirical processes to derive the rate of strong uniform convergence of the kth-nearest neighbor density estimator \(f_ n(x)\) to the true density f(x) on a closed interval J on which f is uniformly bounded above and below. Here \(f_ n(\cdot)\) is based on a sample of size n from density f, \(k=k(n)\) grows with n at a controlled rate, and some differentiability conditions are imposed on f.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 62G15
zbMATH DE Number: 3852218
zbMATH Keywords: density estimates
zbMATH Keywords: Bahadur representation
zbMATH Keywords: Gaussian process
zbMATH Keywords: modulus of continuity
zbMATH Keywords: oscillation
zbMATH Keywords: strong embedding
zbMATH Keywords: empirical processes
zbMATH Keywords: rate of strong uniform convergence
zbMATH Keywords: nearest neighbor density estimator
reviewed by: Eric V. Slud
MaRDI profile type: Publication
cites work: A Note on Quantiles in Large Samples
cites work: On some global measures of the deviations of density function estimates
cites work: Variable Kernel Estimates of Multivariate Densities
cites work: Q5180161
cites work: An approximation of partial sums of independent RV'-s, and the sample DF. I
cites work: A Nonparametric Estimate of a Multivariate Density Function
cites work: Q3662437
cites work: Multivariate k-nearest neighbor density estimates
cites work: Remarks on Some Nonparametric Estimates of a Density Function
cites work: Q3207911
cites work: Weak and strong uniform consistency of the kernel estimate of a density and its derivatives
cites work: The oscillation behavior of empirical processes
cites work: A law of the logarithm for kernel density estimators
cites work: Nonparametric estimates of probability densities
description: scientific article; zbMATH DE number 3852218