Statistics and Its Interface
Volume 10 (2017)
Box dimension estimation of multi-dimensional random fields via wavelet shrinkage
Pages: 207 – 216
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 Hölder 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.
box dimension, Hölder continuity, index-$\beta$ Gaussian field, spatial adaptation, wavelet
2010 Mathematics Subject Classification
Primary 60Dxx, 60G60. Secondary 65Txx.