Spatial data can come in a variety of different forms, but two of the most common generating models for such observations are random fields and point processes. Whilst it is known that spectral analysis can unify these two different data forms, specific methodology for the related estimation is yet to be developed. In this paper, we solve this problem by extending multitaper estimation, to estimate the spectral density matrix function for multivariate spatial data, where processes can be any combination of either point processes or random fields. We discuss finite sample and asymptotic theory for the proposed estimators, as well as specific details on the implementation, including how to perform estimation on non-rectangular domains and the correct implementation of multitapering for processes sampled in different ways, e.g. continuously vs on a regular grid.

翻译：空间数据可以呈现多种不同形式，但此类观测最常见的两种生成模型是随机场和点过程。虽然已知谱分析能够统一这两种不同形式的数据，但相关的特定估计方法学仍有待发展。本文通过扩展多窗谱估计方法解决了这一问题，用于估计多变量空间数据的谱密度矩阵函数，其中过程可以是点过程或随机场的任意组合。我们讨论了所提议估计量的有限样本与渐近理论，以及具体的实现细节，包括如何在非矩形域上执行估计，以及如何正确实现针对不同采样方式（如连续采样与规则网格采样）过程的多窗谱估计。