论文标题
关于多元空间点过程的最小对比度方法
On minimum contrast method for multivariate spatial point processes
论文作者
论文摘要
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和推断提供了一种计算有效的方法。分析复杂的多元点过程模型时，计算时间中的这些相对收益变得更加明显。尽管如此，对多元空间点过程的MC方法几乎没有探索。因此，本文介绍了一种用于参数多元空间点过程的新MC方法。基于猜想的$ K $功能矩阵与其非参数无偏边校正估计器之间差异的功率的痕迹计算对比函数。根据标准假设，我们得出了MC估计器的渐近正态性。通过对双变量log-gaussian cox过程和五变化的产品射击噪声过程的模拟研究证明了所提出的方法的性能。
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.
