Multi-Dimensional Network Function Estimation
N. Mahadevan, Guy P. Nason, Alistair Munro · 2008
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= gi+ isini, where fi= f(ti), gi= g(ti) and i = 1,..., n. Key requirements for this model are that n = 2Jfor some J isin Nopf, data are observed on a regular grid ti= i/n and error term isini~ 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.