Minimum Contrast Parameter Estimation for Fractal Random Fields Based on the Wavelet Periodogram
Maria Dolores Ruiz-Medina, Rosa M. Crujeiras · Communication in Statistics- Theory and Methods · 2011
The weak-consistency of the wavelet periodogram is established for a class of semiparametric fractal Gaussian random fields with local behavior equivalent to the fractional Brownian motion. This result is derived considering a class of isotropic wavelet functions of Haar type. As a consequence, the consistency of a minimum contrast estimator of the fractal parameter, based on the wavelet periodogram, is obtained.