waveband

Computes Bayesian wavelet shrinkage credible intervals for nonparametric regression. The method uses cumulants to derive Bayesian credible intervals for wavelet regression estimates. The first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions. These powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale. Hence, a suitable modification of the discrete wavelet transform allows the posterior cumulants to be found efficiently for any data set. Johnson transformations then yield the credible intervals themselves. Barber, S., Nason, G.P. and Silverman, B.W. (2002) doi:10.1111/1467-9868.00332.