Asymptotically optimal bandwidth selection Of the kernel density estimator under The proportional hazards model

1993 ◽  
Vol 22 (5) ◽  
pp. 1383-1401 ◽  
Author(s):  
J.K. Ghorai ◽  
L.M. Pattanaik
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Bandwidth Selection ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Asymptotically Optimal ◽  
Optimal Bandwidth ◽  
Hazards Model ◽  
Selection Of

scholarly journals X-Entropy: A Parallelized Kernel Density Estimator with Automated Bandwidth Selection to Calculate Entropy

2021 ◽  
Vol 61 (4) ◽  
pp. 1533-1538
Author(s):  
Johannes Kraml ◽  
Florian Hofer ◽  
Patrick K. Quoika ◽  
Anna S. Kamenik ◽  
Klaus R. Liedl
Keyword(s):  
Bandwidth Selection ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Density Estimator

scholarly journals An Improved Variable Kernel Density Estimator Based on L2 Regularization

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2004
Author(s):  
Yi Jin ◽  
Yulin He ◽  
Defa Huang
Keyword(s):  
Probability Distributions ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Estimation Errors ◽  
Optimal Bandwidth ◽  
Lower Estimation ◽  
Data Points ◽  
Integrated Squared Error ◽  
The Given

The nature of the kernel density estimator (KDE) is to find the underlying probability density function (p.d.f) for a given dataset. The key to training the KDE is to determine the optimal bandwidth or Parzen window. All the data points share a fixed bandwidth (scalar for univariate KDE and vector for multivariate KDE) in the fixed KDE (FKDE). In this paper, we propose an improved variable KDE (IVKDE) which determines the optimal bandwidth for each data point in the given dataset based on the integrated squared error (ISE) criterion with the L2 regularization term. An effective optimization algorithm is developed to solve the improved objective function. We compare the estimation performance of IVKDE with FKDE and VKDE based on ISE criterion without L2 regularization on four univariate and four multivariate probability distributions. The experimental results show that IVKDE obtains lower estimation errors and thus demonstrate the effectiveness of IVKDE.

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