Wavelet regression with correlated errors on a piecewise Hölder class

This paper generalizes the methodology of Cai and Brown [Cai, T., Brown, L.D., 1998. Wavelet shrinkage for nonequispaced samples. The Annals of Statistics 26, 1783–1799] for wavelet shrinkage for nonequispaced samples, but in the presence of correlated stationary Gaussian errors. If the true function is a member of a piecewise Hölder class, it is shown that, even for long memory errors, the rate of convergence of the procedure is almost-minimax relative to the independent and identically distributed errors case.