An Algorithm for Optimal Bandwidth Selection for Smooth Nonparametric Quantile Estimation

2002 ◽  
pp. 161-168 ◽  
Author(s):  
Sucharita Ghosh ◽  
Dana Florea-Draghicescu
Keyword(s):  
Bandwidth Selection ◽  
Quantile Estimation ◽  
Optimal Bandwidth ◽  
Selection For ◽  
Nonparametric Quantile Estimation

scholarly journals New Bandwidth Selection for Kernel Quantile Estimators

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Ali Al-Kenani ◽  
Keming Yu
Keyword(s):  
Cross Validation ◽  
Kernel Smoothing ◽  
Bandwidth Selection ◽  
Unbiased Estimation ◽  
Optimal Bandwidth ◽  
Squared Error ◽  
Bandwidth Parameter ◽  
Integrated Squared Error ◽  
Selection For ◽  
Quantile Estimators

We propose a cross-validation method suitable for smoothing of kernel quantile estimators. In particular, our proposed method selects the bandwidth parameter, which is known to play a crucial role in kernel smoothing, based on unbiased estimation of a mean integrated squared error curve of which the minimising value determines an optimal bandwidth. This method is shown to lead to asymptotically optimal bandwidth choice and we also provide some general theory on the performance of optimal, data-based methods of bandwidth choice. The numerical performances of the proposed methods are compared in simulations, and the new bandwidth selection is demonstrated to work very well.

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.

Optimal bandwidth selection for re-substitution entropy estimation

2012 ◽  
Vol 219 (8) ◽  
pp. 3425-3460 ◽  
Author(s):  
Yu-Lin He ◽  
James N.K. Liu ◽  
Xi-Zhao Wang ◽  
Yan-Xing Hu
Keyword(s):  
Bandwidth Selection ◽  
Optimal Bandwidth ◽  
Entropy Estimation ◽  
Selection For
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