Compared to widely used likelihood-based approaches, the minimum contrast (MC) method is a computationally efficient method for estimation and inference of parametric stationary point processes. This advantage becomes more pronounced when analyzing complex point process models, such as multivariate log-Gaussian Cox processes (LGCP). Despite its practical advantages, there is very little work on the MC method for multivariate point processes. The aim of this article is to introduce a new MC method for parametric multivariate stationary spatial point processes. A contrast function is calculated based on the trace of the power of the difference between the conjectured $K$-function matrix and its nonparametric unbiased edge-corrected estimator. Under standard assumptions, the asymptotic normality of the MC estimator of the model parameters is derived. The performance of the proposed method is illustrated with bivariate LGCP simulations and a real data analysis of a bivariate point pattern of the 2014 terrorist attacks in Nigeria.

翻译：与广泛使用的基于似然的方法相比，最小对比（MC）方法是一种针对参数平稳点过程进行估计和推断的计算高效方法。这一优势在分析复杂点过程模型（如多元对数高斯Cox过程（LGCP））时尤为突出。尽管具有实际优势，但目前关于多元点过程MC方法的研究非常有限。本文旨在引入一种新的针对参数多元平稳空间点过程的MC方法。对比函数基于假设的$K$函数矩阵与其非参数无偏边界校正估计量之间幂的迹进行计算。在标准假设下，推导了模型参数MC估计量的渐近正态性。通过双变量LGCP模拟以及对2014年尼日利亚恐怖袭击双变量点模式的实际数据分析，展示了所提出方法的性能。