Detection of suspicious areas in non-stationary Gaussian fields and locally averaged non-Gaussian linear fields

Abstract

Gumbel-type extreme value theory for arrays of discrete Gaussian random fields is studied and applied to some classes of discretely sampled approximately locally self-similar Gaussian processes, especially micro-noise models. Non-Gaussian discrete random fields are handled by considering the maximum of local averages of raw data or residuals. Based on some novel weak approximations with rate for (weighted) partial sums for spatial linear processes including results under a class of local alternatives, sufficient conditions for Gumbel-type asymptotics of maximum-type detection rules to detect peaks and suspicious areas in image data and, more generally, random field data, are established. The results are examined by simulations and illustrated by analyzing CT brain image data.