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Article Dans Une Revue Spatial Statistics Année : 2022

A convolution type model for the intensity of spatial point processes applied to eye-movement data

Résumé

Estimating the first-order intensity function in point pattern analysis is an important problem, and it has been approached so far from different perspectives: parametrically, semiparametrically or nonparametrically. Our approach is close to a semiparametric one. Motivated by eye-movement data, we introduce a convolution type model where the log-intensity is modeled as the convolution of a function $\beta(\cdot)$, to be estimated, and a single spatial covariate (the image an individual is looking at for eye-movement data). Based on a Fourier series expansion, we show that the proposed model can be viewed as a log-linear model with an infinite number of coefficients, which correspond to the spectral decomposition of $\beta(\cdot)$. After truncation, we estimate these coefficients through a penalized Poisson likelihood. We illustrate the efficiency of the proposed methodology on simulated data and on eye-movement data.

Dates et versions

hal-04367339 , version 1 (30-12-2023)

Identifiants

Citer

Jean-François Coeurjolly, Francisco Cuevas-Pacheco, Marie-Hélène Descary. A convolution type model for the intensity of spatial point processes applied to eye-movement data. Spatial Statistics, 2022, 51 (3), pp.100651. ⟨10.1016/j.spasta.2022.100651⟩. ⟨hal-04367339⟩
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