Wavelet-based estimations of fractional Brownian sheet: Least squares versus maximum likelihood

摘要

The scaling behavior (or self-similarity and long-range dependence) has been studied in numerous fields such as computer, telecommunication, hydrology and economics, and can be characterized by the Hurst parameter H. Fractional Brownian sheet plays an important role in modeling the scaling behavior in multi-dimensional signals. A wavelet-based maximum likelihood estimator for the Hurst parameter H = (H-1, ..., H-d) of fractional Brownian sheet is proposed. It is asymptotically normal and compared with the wavelet-based least squares estimators introduced in the previous article from theoretical analysis and numerical simulation. The theoretical results show that the proposed estimator has the same asymptotic covariance as the least squares estimator of which the weight is equal to the number of available wavelet coefficients and the convergence rates of two estimators are both O(1/root Pi T-d(i=1)i).T-i is sample length in the ith dimension. The simulation results show that the proposed estimator performs better than the least squares estimators in bias and costs less runtime than the generalized least squares estimator realized by the two-step method. (C) 2019 Elsevier B.V. All rights reserved.