  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.
