Palm distributions of superposed point processes for statistical inference

• 成果类型: Article
• 署名作者: Beraha, M.; Camerlenghi, F.; Ghilotti, L.
• 署名单位: University of Milano-Bicocca; Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asag021
• 发表日期: 2026
• 页码: asag021
• 关键词: Mat & eacute; rn cluster process; Minimum contrast estimation; Noisy observation; Shot noise Cox process; Summary statistic; Superposition of point processes; PROCESS MODELS

摘要

Palm distributions play a central role in the study of point processes and their associated summary statistics. In this work, we characterize the Palm distributions of the superposition of independent point processes, establishing a simple mixture representation depending on the point processes' Palm distributions and moment measures. We explore two statistical applications enabled by our main result. First, we consider minimum contrast estimation for corrupted point processes. Second, we investigate the class of shot noise Cox processes and derive explicit expressions for their higher-order Palm distributions. In the finite case, we further obtain a tractable expression for the Janossy density, which plays the role of a likelihood function and thus can be used for new likelihood-based inference strategies. Extensions to the superposition of multiple point processes and to higher-order Palm distributions are also presented.