Marked point processes intensity estimation using sparse group Lasso method applied to locations of lucrative and cooperative banks in mainland France

TL;DR

This paper models the spatial distribution of major banks in France, revealing clustering patterns and proposing a sparse group Lasso method for intensity estimation using socio-economic covariates.

Contribution

It introduces a novel group-penalized likelihood approach for bivariate point process intensity estimation incorporating socio-economic data.

Findings

Banks exhibit significant clustering at small scales.

The proposed method effectively estimates intensity functions with covariates.

Insights into the distinct behavior of cooperative banks within the sector.

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.