A2016
Title: Balancing the edge effect and dimension of spectral spatial statistics
Authors: Anne van Delft - Columbia University (United States) [presenting]
Holger Dette - Ruhr-Universitaet Bochum (Germany)
Abstract: Distributional properties of a class of spectral spatial statistics are investigated under irregular sampling of a random field defined on Rd, and used to obtain a novel test for isotropy via a minimum distance approach. More precisely, an explicit expression for the minimum L2-distance between the spectral density of the random field and its best approximation by a spectral density of an isotropic process is derived in terms of certain integrals of the spectral density, which are then estimated from the data. Within this context, edge effects are well-known to create a bias in classical estimators commonly encountered in the analysis of spatial data. This bias increases with dimension $d$ and, for $d>1$, can become non-negligible in the limiting distribution of such statistics to the extent that a nondegenerate distribution does not exist. A general theory is provided for a class of integrated spectral statistics that are used to estimate the minimum $L_2-$distance, which enables: 1) significantly reducing this bias and 2) ensuring that asymptotically Gaussian limits can be derived for $d\le 3$ for appropriately tapered versions of such statistics. This theory addresses crucial gaps in the literature and demonstrates that tapering with a sufficiently smooth function is necessary to achieve such results.
