Abstract: We investigate the global performances of non-linear wavelet estimation in regression models with correlated errors. Convergence properties are studied over a wide range of Besov classes and for a variety of error measures. We consider error distributions with Long-Range-Dependence parameter . In this setting we present a single adaptive wavelet thresholding estimator which achieves near-optimal properties simultaneously over a class of spaces and error measures. Our method reveals an elbow feature in the rate of convergence at when . Using a vaguelette decomposition of fractional Gaussian noise we draw a parallel with certain inverse problems where similar rate results occur.
Key words and phrases: Adaptation, correlated data, deconvolution, degree of ill posedness, fractional Brownian Motion, fractional differentiation, fractional integration, inverse problems, linear processes, long range dependence, Lᵖ loss, maxisets, Meyer wavelet, nonparametric regression, vaguelettes, WaveD.