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, f
ⁱ
= 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, sigma
²
). 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.