Estimation of self-similar Gaussian fields using wavelet transform

Abstract

We propose an estimator [Formula: see text] for the Hurst parameters [Formula: see text] of fractional Brownian sheet (FBS), which plays an important role in modeling anisotropic self-similar Gaussian fields. The proposed estimator is based on the stationarity and scale invariance of hyperbolic wavelet coefficients of FBS and the weighted least squares. We use simulated fields to validate the proposed estimator. The estimator performs well in both the standard deviation and the root mean square error.