Compared to widely used likelihood-based approaches, the minimum contrast (MC) method offers a computationally efficient method for estimation and inference of spatial point processes. These relative gains in computing time become more pronounced when analyzing complicated multivariate point process models. Despite this, there has been little exploration of the MC method for multivariate spatial point processes. Therefore, this article introduces a new MC method for parametric multivariate spatial point processes. A contrast function is computed 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, we derive the asymptotic normality of our MC estimator. The performance of the proposed method is demonstrated through simulation studies of bivariate log-Gaussian Cox processes and five-variate product-shot-noise Cox processes.

翻译：与广泛使用的基于似然的方法相比，最小对比度（MC）方法为空间点过程的估计与推断提供了一种计算高效的方法。在分析复杂的多元点过程模型时，这些计算时间上的相对优势变得更为显著。尽管如此，针对多元空间点过程的MC方法仍鲜有探索。因此，本文针对参数化多元空间点过程提出了一种新的MC方法。对比度函数是基于推测的$K$函数矩阵与其非参数无偏边缘校正估计量之差的幂的迹来计算的。在标准假设下，我们推导了MC估计量的渐近正态性。通过模拟研究二元对数高斯Cox过程和五元乘积散粒噪声Cox过程，验证了所提方法的性能。