Optimal bandwidth selection for kernel density functionals estimation
type: Item
instance of: scholarly article
title: Optimal bandwidth selection for kernel density functionals estimation
zbMATH Open document ID: 1426.62112
DOI: 10.1155/2015/242683
published in: Journal of Probability and Statistics
publication date: 2018-08-14T00:00:00Z
review text: Summary: The choice of bandwidth is crucial to the kernel density estimation (KDE) and kernel based regression. Various bandwidth selection methods for KDE and local least square regression have been developed in the past decade. It has been known that scale and location parameters are proportional to density functionals \(\int \gamma(x) f^2(x) d x\) with appropriate choice of \(\gamma(x)\) and furthermore equality of scale and location tests can be transformed to comparisons of the density functionals among populations. \(\int \gamma(x) f^2(x) d x\) can be estimated nonparametrically via kernel density functionals estimation (KDFE). However, the optimal bandwidth selection for KDFE of \(\int \gamma(x) f^2(x) d x\) has not been examined. We propose a method to select the optimal bandwidth for the KDFE. The idea underlying this method is to search for the optimal bandwidth by minimizing the mean square error (MSE) of the KDFE. Two main practical bandwidth selection techniques for the KDFE of \(\int \gamma(x) f^2(x) d x\) are provided: Normal scale bandwidth selection (namely, ``Rule of Thumb'') and direct plug-in bandwidth selection. Simulation studies display that our proposed bandwidth selection methods are superior to existing density estimation bandwidth selection methods in estimating density functionals.
Mathematics Subject Classification ID: 62G07
zbMATH DE Number: 6917451
Wikidata QID: Q59114208
author: S. Chen
describes a project that uses: KernSmooth
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/242683
OpenAlex ID: W1551760581
cites work: Nonparametric estimation of the location and scale parameters based on density estimation
cites work: Estimation of Location and Scale Parameters Based on Kernel Functional Estimators
cites work: A note on the estimation of the integral of \(f^ 2(x)\)
cites work: Nonparametric Confidence Intervals for a Shift Parameter
cites work: Estimation of density functionals
cites work: Q4727203
cites work: Q4272483
cites work: A comparative study of some kernel-based nonparametric density estimators
cites work: A Brief Survey of Bandwidth Selection for Density Estimation
cites work: Bandwidth selection: Classical or plug-in?
cites work: Q4865051
cites work: Biased and Unbiased Cross-Validation in Density Estimation
cites work: Optimal bandwidth selection in nonparametric regression function estimation
cites work: On the Integral Mean Square Error of Some Nonparametric Estimates for the Density Function
cites work: On Choosing a Delta-Sequence
cites work: Smoothed cross-validation
cites work: Q3729827
cites work: Local Bandwidth Selection for Kernel Estimates
cites work: On optimal data-based bandwidth selection in kernel density estimation
cites work: A Flexible and Fast Method for Automatic Smoothing
cites work: An Effective Bandwidth Selector for Local Least Squares Regression
cites work: Q3125064
cites work: Scale measures for bandwidth selection
cites work: Q4863755
cites work: The performance of six popular bandwidth selection methods on some real data sets
cites work: Czekanowski's Index of Overlap, itsLp-Type Extension, and BIAS Reduction
cites work: Q3999009
cites work: A Note on the Ratio of Two Normally Distributed Variables
Recommended article: Bandwidth selection for kernel density estimation
Recommended article: On optimal data-based bandwidth selection in kernel density estimation
Recommended article: On bandwidth selection in kernel density estimation
Recommended article: A bandwidth selection for kernel density estimation of functions of random variables
Recommended article: Optimal bandwidths for kernel density estimators of functions of observations
Recommended article: Bandwidth selection for kernel distribution function estimation
description: scientific article; zbMATH DE number 6917451