Box dimension estimation of multi-dimensional random fields via wavelet shrinkage

摘要

Computation of the box dimension for high-dimensional surfaces is much more complicated than the one-dimensional case. To obtain a fast computation, we employ the relationship between the box dimension and the wavelet coefficients of a surface through the local oscillation. This approach gives an appropriate consistent estimator of box dimension for noisy paths. The behavior of convergence is also studied under Holder continuity assumption for the family of index-beta Gaussian fields. We show that the precision of the estimation procedure is not affected by the growth of dimension of the sample path. We finally examine the properties of the proposed estimator using a simulation study and a real dataset on equlibration of a particular solution.