scholarly journals Infill asymptotics for adaptive kernel estimators of spatial intensity

2021 ◽  
Author(s):  
M.N.M. van Lieshout
Keyword(s):  
Kernel Estimators ◽  
Infill Asymptotics ◽  
Spatial Intensity ◽  
Adaptive Kernel

scholarly journals Infill Asymptotics and Bandwidth Selection for Kernel Estimators of Spatial Intensity Functions

2019 ◽  
Vol 22 (3) ◽  
pp. 995-1008
Author(s):  
M. N. M. van Lieshout
Keyword(s):  
Point Process ◽  
Mean Squared Error ◽  
Bandwidth Selection ◽  
Intensity Function ◽  
Kernel Estimators ◽  
Infill Asymptotics ◽  
Squared Error ◽  
Selection For ◽  
Asymptotic Mean Squared Error ◽  
Intensity Functions

AbstractWe investigate the asymptotic mean squared error of kernel estimators of the intensity function of a spatial point process. We derive expansions for the bias and variance in the scenario that n independent copies of a point process in $\mathbb {R}^{d}$ ℝ d are superposed. When the same bandwidth is used in all d dimensions, we show that an optimal bandwidth exists and is of the order n− 1/(d+ 4) under appropriate smoothness conditions on the true intensity function.

scholarly journals A Novel Neuron in Kernel Domain

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zahra Khandan ◽  
Hadi Sadoghi Yazdi
Keyword(s):  
Neural Network ◽  
Online Learning ◽  
Mean Square ◽  
Least Mean Square ◽  
Backpropagation Neural Network ◽  
Adaptive Parameters ◽  
Kernel Parameter ◽  
Online Learning Algorithms ◽  
Adaptive Kernel ◽  
Kernel Least Mean Square

Kernel-based neural network (KNN) is proposed as a neuron that is applicable in online learning with adaptive parameters. This neuron with adaptive kernel parameter can classify data accurately instead of using a multilayer error backpropagation neural network. The proposed method, whose heart is kernel least-mean-square, can reduce memory requirement with sparsification technique, and the kernel can adaptively spread. Our experiments will reveal that this method is much faster and more accurate than previous online learning algorithms.

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