Journal of Quality Engineering and Management

A novel approach to nonparametric estimation of the intensity function of spatial Poisson point processes and its application in estimating the Intensity of Inga Sapindoides trees

Document Type : Original Article

Authors

mitra hasheminia 1
Reza pourtaheri 2

1 Department of Statistics, Allameh Tabataba’i University, Tehran, Iran

2 Department of Statistics, Allameh Tabataba'i University, Tehran,Iran

https://doi.org/10.48313/jqem.2023.199824
Abstract
Modelling and estimating the intensity function of a point pattern is one of the preliminary and fundamental issues in inference of point processes, and it considered as a prerequisite for many other problems. It has been addressed from different perspectives. With the rapid development of data-collection technologies, a wide range of data has been produced, and considering covariates has been a big step forward in the theory of point processes, which has mainly been addressed from a parametric perspective.

In this paper, we introduce a novel approach for nonparametrically estimating the intensity of an inhomogeneous Poisson point process, which is an unknown function of several independent spatial covariates. In the proposed method, using the approximation technique of radial basis function for unknown multivariate functions, the nonparametric model of the intensity function is transformed into a log-linear model. Since the accuracy of the multivariate function approximation directly affects the accuracy of the intensity function estimate, we enhance the nonparametric estimation quality of the intensity function in spatial Poisson point processes by optimizing the shape parameter of the radial basis function through minimizing the Bayesian information criterion.

Keywords

Approximate maximum likelihood estimate
Multivariate function approximation
Pixel counts
Inhomogeneous spatial Poisson point process
Independent spatial covariates
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Journal of Quality Engineering and Management
Volume 13, Issue 3
Autumn 2023
Pages 317-334

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