Wavelet Estimation of an Unknown Function Observed with Correlated Noise

In many practical applications of nonparametric regression, it is desirable to

allow for the possibility that the noise is correlated. In this paper, we focus

on wavelet-based nonparametric function estimation and propose two distinct

methods for estimating the correlation structure of the noise, one based in the

time domain and the other based in the wavelet domain. Once the correlation

structure has been estimated, there are various methods that may be used for

reconstructing the unknown signal; we focus here on the empirical Bayes block

shrinkage method proposed by Wang and Wood (2006). A simulation study is

described. Our numerical results indicate that the proposed methods do a good

job of reconstructing the signal even when the noise is highly correlated.