Multi-Dimensional Network Function Estimation

We apply a non-parametric regression technique based on second generation wavelets to irregularly spaced network data. Conventional wavelet based non-parametric regression can be modelled as, fⁱ = g_i + isin_i, where f_i = f(t_i), g_i = g(t_i) and i = 1,..., n. Key requirements for this model are that n = 2^J for some J isin Nopf, data are observed on a regular grid t_i = i/n and error term isin_i ~ N(0, sigma²). Communication networks have irregularities that standard wavelet regression cannot handle. We adopt the technique developed by Jansen et al [7], called "lifting one coefficient at a time", for irregularly spaced network data. We demonstrate the linear shrinkage and non-linear single coefficient shrinkage induces large bias in the estimation. We propose a new \´across-scale\´ block shrinkage method for coefficient processing that produces much better estimates.