Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 517–543 | Cite as

A quadrat neighborhood estimator for intensity function of point processes

  • Azam Dehghani
  • Mohammad Q. Vahidi-AslEmail author
Original Research


In nonparametric estimation of the intensity function of a point process, assigning the local event weight is particularly important. This paper describes a sequential quadrat partitioning of the study region to define a quadrat neighborhood of a point. Based on this idea, a quadrat neighborhood estimator of intensity function is introduced. We extend this method to estimate the product density. Meanwhile, we show that under infill asymptotics our proposed estimator is asymptotically unbiased for inhomogeneous Poisson point process. Simulations are also used to investigate the performance of our proposed estimator.


Nonparametric estimation Adaptive estimation Point process Intensity function Product density 

Mathematics Subject Classification

62G05 62G99 60G55 


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.Department of StatisticsShahid Beheshti UniversityEvin, TehranIran

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