Wavelet regression with correlated errors on a piecewise Hölder class

Rogério F. Porto, Pedro A. Morettin and Elisete C.Q. Aubin

Statistics & Probability Letters, 2008, vol. 78, issue 16, 2739-2743

Abstract: 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.

Date: 2008
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