Computation and application of robust data-driven bandwidth selection for gradient function estimation

2019 ◽  
Vol 361 ◽  
pp. 274-293 ◽  
Author(s):  
Qichang Xie ◽  
Qiankun Sun
Keyword(s):  
Bandwidth Selection ◽  
Data Driven ◽  
Function Estimation ◽  
Gradient Function ◽  
Selection For

scholarly journals Optimal bandwidth selection for recursive Gumbel kernel density estimators

2019 ◽  
Vol 7 (1) ◽  
pp. 375-393
Author(s):  
Yousri Slaoui
Keyword(s):  
Probability Density Function ◽  
Strong Consistency ◽  
Bandwidth Selection ◽  
Kernel Density ◽  
Kernel Estimator ◽  
Data Driven ◽  
Kernel Estimators ◽  
Convergence Properties ◽  
Selection For ◽  
Selection Of

AbstractIn this paper, we propose a data driven bandwidth selection of the recursive Gumbel kernel estimators of a probability density function based on a stochastic approximation algorithm. The choice of the bandwidth selection approaches is investigated by a second generation plug-in method. Convergence properties of the proposed recursive Gumbel kernel estimators are established. The uniform strong consistency of the proposed recursive Gumbel kernel estimators is derived. The new recursive Gumbel kernel estimators are compared to the non-recursive Gumbel kernel estimator and the performance of the two estimators are illustrated via simulations as well as a real application.

scholarly journals Graphics processing units in acceleration of bandwidth selection for kernel density estimation

2013 ◽  
Vol 23 (4) ◽  
pp. 869-885 ◽  
Author(s):  
Witold Andrzejewski ◽  
Artur Gramacki ◽  
Jarosław Gramacki
Keyword(s):  
Graphics Processing Units ◽  
Bandwidth Selection ◽  
Kernel Density ◽  
Data Driven ◽  
Density Estimator ◽  
Algorithmic Optimization ◽  
Bandwidth Parameter ◽  
Selection For ◽  
Graphics Processing ◽  
Probability Density Function Pdf

Abstract The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.

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