González Pérez, IgnacioBorrajo García, María IsabelGonzález Manteiga, Wenceslao2025-02-032025-02-032025-01-27González-Pérez, I., Borrajo, M.I. & González-Manteiga, W. Nonparametric testing of first-order structure in point processes on linear networks. Stat Papers 66, 42 (2025). https://doi.org/10.1007/s00362-024-01657-80932-5026https://hdl.handle.net/10347/39459In this paper we address a two-sample problem in the context of point processes on linear networks. The aim is to determine whether two given point patterns defined over the same linear network and under the assumption of Poissonness, share the same spatial structure. To do so, a Kolmogorov–Smirnov and a Cramér von Mises type test statistics are developed and analysed through an extensive simulation study. We have included different types of networks, balanced and unbalanced sample sizes, and homogeneous and inhomogeneous Poisson point processes. The results show a good level adjustment and high power values, the latter increasing with the sample size and the discrepancy between the two generating intensities. Finally, these methods have also been applied to the analysis of traffic accidents in Rio de Janeiro (Brazil), studying their distribution at different rush hours.eng©TheAuthor(s) 2025. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.journal article10.1007/s00362-024-01657-81613-9798open access