Large deviations and moderate deviations for kernel density estimators of directional data
type: Item
instance of: scholarly article
title: Large deviations and moderate deviations for kernel density estimators of directional data
zbMATH Open document ID: 1213.60055
author: Lina Li
author: Fuqing Gao
publication date: 2010-10-04T00:00:00Z
review text: Let \(f_n\) be the non-parametric kernel density estimator of directional data based on a kernel function \(K\) and a sequence of iid random variables taking values in the \(d\)-dimensional unit sphere \(S^{d-1}\). This paper studies uniform large deviations and uniform moderate deviations for \(f_n\) by the empirical process approach. It is assumed that the kernel is a function of bounded variation and the density of the random variables is continuous.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 5795523
zbMATH Keywords: kernel density estimator
zbMATH Keywords: directional data
zbMATH Keywords: moderate deviations
zbMATH Keywords: large deviations
reviewed by: Pedro A. Morettin
MaRDI profile type: Publication
full work available at URL: s10114-010-7205-9
OpenAlex ID: W2000698863
cites work: Q5656211
cites work: Q3790478
cites work: Kernel density estimation with spherical data
cites work: Kernel estimators of density function of directional data
cites work: Q3999358
cites work: Central limit theorem for integrated square error of kernel estimators of spherical density
cites work: Laws of the iterated logarithm for kernel estimator of density function of spherical data
cites work: An empirical process approach to the uniform consistency of kernel-type function estimators
cites work: Moderate deviations and large deviations for kernel density estimators
cites work: On consistency of kernel density estimators for randomly censored data: Rates holding uniformly over adaptive intervals
cites work: Large deviations for a general class of random vectors
cites work: U-processes: Rates of convergence
cites work: On general minimax theorems
cites work: Q4391441
cites work: Moderate deviations and law of the iterated logarithm in \(L_1(\mathbb R^d)\) for kernel density estimators
cites work: Rates of strong uniform consistency for multivariate kernel density estimators. (Vitesse de convergence uniforme presque sûre pour des estimateurs à noyaux de densités multivariées)
cites work: Large Deviations Limit Theorems for the Kernel Density Estimator
cites work: New concentration inequalities in product spaces
DOI: 10.1007/S10114-010-7205-9
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5795523