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 ROBUST GENERALIZED METHOD OF MOMENTS ESTIMATION

2014 ◽  
Vol 31 (5) ◽  
pp. 1054-1077 ◽  
Author(s):  
Daniel Wilhelm
Keyword(s):  
Method Of Moments ◽  
Mean Squared Error ◽  
Order Approximation ◽  
Generalized Method Of Moments ◽  
Bandwidth Selection ◽  
Estimation Procedure ◽  
Point Estimate ◽  
Optimal Bandwidth ◽  
Squared Error ◽  
Method Of Moments Estimation

A two-step generalized method of moments estimation procedure can be made robust to heteroskedasticity and autocorrelation in the data by using a nonparametric estimator of the optimal weighting matrix. This paper addresses the issue of choosing the corresponding smoothing parameter (or bandwidth) so that the resulting point estimate is optimal in a certain sense. We derive an asymptotically optimal bandwidth that minimizes a higher-order approximation to the asymptotic mean-squared error of the estimator of interest. We show that the optimal bandwidth is of the same order as the one minimizing the mean-squared error of the nonparametric plugin estimator, but the constants of proportionality are significantly different. Finally, we develop a data-driven bandwidth selection rule and show, in a simulation experiment, that it may substantially reduce the estimator’s mean-squared error relative to existing bandwidth choices, especially when the number of moment conditions is large.

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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