Uniformly Consistent Autoregressive Spectral Estimates for Stationary Spatial Processes on a D-Dimensional Lattice

• Activity Number: 229
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Abhimanyu Gupta*+ and Peter Robinson
• Companies: University of Essex and LSE
• Keywords: Spectral density ; Lattice data ; Spatial statistics ; Covariance matrix ; Uniform Consistency ; Toeplitz

Abstract

Autoregressive spectral density estimation for stationary random fields on a regular spatial lattice has the advantage of providing a guaranteed positive-definite estimate even when suitable edge-effect correction is employed. Such processes have an infinite autoregressive (AR) representation if they are also purely non-deterministic. This paper uses truncated versions of the AR representation to estimate the spectral density. The truncation length is allowed to diverge in all dimensions in order to avoid the potential bias which would accrue due to truncation at a fixed lag-length. The covariance structure of stationary random fields defined on regularly spaced d-dimensional lattices is studied in detail and the covariance matrix is shown to satisfy a generalization of the Toeplitz property familiar from time series analysis. Using this property, uniform consistency of the spectral density estimate is established.