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Marked point processes intensity estimation using sparse ...
[Submitted on 29 Dec 2025 (v1), last revised 22 Jul 2026 (this v · 2025-12-29 · via math.ST updates on arXiv.org

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Abstract:In this paper, we model the locations of five major banks in mainland France, two lucrative and three cooperative institutions based on socio-economic considerations. Locations of banks are collected using web scrapping and constitute a bivariate spatial point process for which we estimate nonparametrically summary functions (intensity, Ripley and cross-Ripley's K functions). This shows that the pattern is highly inhomogenenous and exhibits a clustering effect especially at small scales, and thus a significant departure to the bivariate (inhomogeneous) Poisson point process is pointed out. We also collect socio-economic datasets (at the living area level) from INSEE and propose a parametric modelling of the intensity function using these covariates. We propose a group-penalized bivariate composite likelihood method to estimate the model parameters, and we establish its asymptotic properties. The application of the methodology to the banking dataset provides new insights into the specificity of the cooperative model within the sector, particularly in relation to the theories of institutional isomorphism.

Submission history

From: Jean-Francois Coeurjolly [view email] [via CCSD proxy]
[v1] Mon, 29 Dec 2025 08:26:57 UTC (4,060 KB)
[v2] Wed, 22 Jul 2026 09:45:21 UTC (7,859 KB)