Two-dimensional spectral analysis for marked point processes

Spectral analysis has already been shown to be a powerful tool in the interrogation of lattice patterns, since it assumes no structural characteristics in the data (such as isotropy) prior to analysis. Here we extend the analysis to non-lattice data for which both points and marks can exhibit spatial structure. Both distance- and spectral-based measures are introduced, and theoretical comparisons are made between lattice and mark spectra. Simulated examples suggest a high degree of independence between point and mark spectra, and a real example is presented for the spatial structure of 584 tree locations and diameters at breast height of longleaf pine trees in southern Georgia.