Spatial circular matrices, with applications - Grant Hillier; Federico Martellosio (Centre for Microdata Methods and Practice (cemmap), 2010)
The cumulants of the quadratic forms associated to the so-called spatial design matrices are often needed for inference in the context of isotropic processes on uniform grids. Unfortunately, because the eigenvalues of the matrices involved are generally unknown, the computation of the cumulants may be very demanding if the grids are large. This paper constructs circular counterparts, with known eigenvalues, to the spatial design matrices. It then studies some of their properties, and analyzes their performance in a number of applications.
Keywords: C12; C21; 330; circulant matrices; isotropic spatial processes; Moran correlogram; quadratic forms; spatial design matrices; variogram GLS fitting; Statistischer Test; Ökonometrie