Tail Estimation of the Spectral Density under Fixed Domain Asymptotics
Conference
Format: IPS Abstract
Session: Invited Session 9A - Recent Advancements in Spatial and Spatiotemporal Statistics
Thursday 5 December 9:30 a.m. - 11 a.m. (Australia/Adelaide)
Abstract
Many estimation studies have been conducted using fixed-domain asymptotics for spatial processes. However, most have been studied under the spatial domain approach, in which specific covariance models are assumed. Unlike the spatial domain approach, spectral density is one way to describe the spatial dependence for weakly stationary spatial processes. A methodology is proposed to simultaneously estimate parameters that describe the tail behavior of spectral densities under fixed domain asymptotics. The spectral tail parameters are defined by assuming only a tail structure of the spectral densities, which can involve a broader class of spatial dependence models. Theoretical properties of the proposed estimator, such as consistency and asymptotic results, are introduced. Meanwhile, simulation experiments with real data studies have also been shown to support theoretical studies.