Wavelet variances

[stephaneguerrier]

Hi guys,

Once Issue #4 has been addressed the next part is to compute various statistics from the wavelet decomposition, here are the main ones:

• [x] Classical wavelet variance: this is the classical estimator proposed by Percival. This is already implemented in the gmwm package. This should be straightforward.
• [x] Robust wavelet variance: this robust estimator @robertomolinari and I proposed. This is also implemented on the gmwm package. However, it might be good to double check that and in particular the covariance matrix. @robertomolinari: could you add some details here?
• [ ] Spatial (robust) wavelet variance: This should identical to the first two points. The only difference is that wavelet variance should be computed on a vectorized version of the spatial wavelet decomposition. If the first two points are addressed this should be simple. @robertomolinari : could you add some details here (if needed!) Thanks!
• [x] Cross-covariance: This is the covariance between two wavelet transforms. @HaotianXu: could you please add some details here? Thanks!

Note that for all the quantities described above we will need to compute the point estimate together with its (estimated) variance.