Optimal bandwidth selection for variable kernel density estimates

2005 ◽  
Vol 74 (2) ◽  
pp. 116-128 ◽  
Author(s):  
Alain Berlinet ◽  
Gérard Biau ◽  
Laurent Rouvière
Keyword(s):  
Bandwidth Selection ◽  
Kernel Density ◽  
Variable Kernel ◽  
Density Estimates ◽  
Optimal Bandwidth ◽  
Kernel Density Estimates ◽  
Selection For

scholarly journals Optimal Bandwidth Selection for Kernel Density Functionals Estimation

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Su Chen
Keyword(s):  
Density Estimation ◽  
Bandwidth Selection ◽  
Kernel Density ◽  
Least Square ◽  
Density Functionals ◽  
Selection Methods ◽  
Optimal Bandwidth ◽  
Location Parameters ◽  
The Mean ◽  
Selection For

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∫γ(x)f2(x)dxwith appropriate choice ofγ(x)and furthermore equality of scale and location tests can be transformed to comparisons of the density functionals among populations.∫γ(x)f2(x)dxcan be estimated nonparametrically via kernel density functionals estimation (KDFE). However, the optimal bandwidth selection for KDFE of∫γ(x)f2(x)dxhas 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∫γ(x)f2(x)dxare 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.

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