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

M.N.M. van Lieshout*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

24 Downloads (Pure)

Abstract

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 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.

Original languageEnglish
Pages (from-to)995-1008
Number of pages14
JournalMethodology and computing in applied probability
Volume22
Issue number3
Early online date28 Nov 2019
DOIs
Publication statusPublished - 1 Sep 2020

Keywords

  • UT-Hybrid-D
  • Infill asymptotics
  • Intensity function
  • Kernel estimator
  • Mean squared error
  • Point process
  • Bandwidth

Fingerprint Dive into the research topics of 'Infill Asymptotics and Bandwidth Selection for Kernel Estimators of Spatial Intensity Functions'. Together they form a unique fingerprint.

Cite this