Palm distributions of superposed point processes for statistical inference
研究了独立点过程叠加后的Palm分布，得到简单混合表示，并用于受损点过程的最小对比度估计和shot noise Cox过程的高阶Palm分布推导，为似然推断提供新方法。
Abstract 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.