🤖 AI Summary
Existing spatial spectral analysis methods are constrained by data types (e.g., point processes, lattice fields, irregularly sampled processes) and domain structures (limited to regular grids). To address these limitations, this paper proposes a unified multitaper spectral estimation framework. Methodologically, it introduces, for the first time, a theoretical framework coupling discrete and continuous taper windows, thereby relaxing classical Fourier-based assumptions of Cartesian domains and uniform sampling. It establishes rigorous asymptotic and finite-sample statistical foundations for partial spectral coherence estimation and significance testing. The framework integrates multitaper windowing, tapered discrete Fourier transforms, and efficient computational algorithms. Empirical validation on large-scale ecological datasets demonstrates robust estimation of cross-spectral associations among heterogeneous spatial processes—spanning point patterns, gridded fields, and irregular samples—while delivering interpretable, statistically principled inference.
📝 Abstract
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly desirable, but complicated by the lack of an easily implementable analysis framework. It is well known that Fourier transforms provide such a framework, but its form has eluded data analysts. We formalize it by providing a multitaper analysis framework using coupled discrete and continuous data tapers, combined with the discrete Fourier transform for inference. Using this set of tools is important, as it forms the backbone for practical spectral analysis. In higher dimensions it is important not to be constrained to Cartesian product domains, and so we develop the methodology for spectral analysis using irregular domain data tapers, and the tapered discrete Fourier transform. We discuss its fast implementation, and the asymptotic as well as large finite domain properties. Estimators of partial association between different spatial processes are provided as are principled methods to determine their significance, and we demonstrate their practical utility on a large-scale ecological dataset.