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

  • M. N. M. van LieshoutEmail author
Open Access


We 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 \(\mathbb {R}^{d}\) 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.


Bandwidth Infill asymptotics Intensity function Kernel estimator Mean squared error Point process 

Mathematics Subject Classification (2010)

60G55 62G07 60D05 



We are grateful to the referee and associate editor for their careful reading of the manuscript.


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© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.CWIAmsterdamThe Netherlands
  2. 2.University of TwenteEnschedeThe Netherlands

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