Nonlinear log-wavelet-variance regression for perturbed 2D long memory Gaussian random fields

In this paper, we apply the wavelet method to the estimation of the memory parameter of a two-dimensional (intrinsically) stationary Gaussian long memory random field, which is perturbed by an independent, additive and stationary Gaussian short memory noise field. We propose the nonlinear log-wavelet-variance regression (NLWVR) estimator, and determine its consistency with convergence rate as well as asymptotic normality, basically when the memory parameter of the signal field is larger than −1. The finite sample performance of the NLWVR estimator of perturbed stationary long memory random fields is examined by Monte Carlo simulation. In the simulation, we also include the comparison between the NLWVR estimator and the classic wavelet-variance-based linear regression estimator.