Variance Estimation of Spectral Statistics for Spatial Processes using Subsampling

Oregon Convention Center 

In the realm of frequency domain analysis for spatial data, estimators based on the periodogram often exhibit complex variance structures originating from aggregated periodogram covariances. Previous attempts to bootstrap these statistics face challenges in capturing these variances and quantifying estimation uncertainty. This difficulty arises because achieving consistency for various periodogram-based statistics requires evaluating the periodogram at an increasing number of frequencies as the sample size grows. Despite the diminishing dependence between periodogram ordinates, the decay rate balances the growing frequencies, preserving a dependence structure in the limiting distribution. Consequently, the validity of frequency domain bootstrap (FDB) approaches for spatial data is confined to a specific class of processes and statistics. To overcome this challenge, we propose cutting-edge FDB methods based on subsampling which can accurately capture uncertainty without necessitating additional stringent assumptions beyond those required for the existence of a target limit distribution, filling a gap in the theory by providing distributional approximations for spectral statistics.

Frequency Domain Bootstrap

Periodogram

Subsampling

Spatial Process

Spectral Mean Statistic 

Section on Statistics and the Environment