Lp wavelet regression with correlated errors. Statist. Sinica

Abstract: We investigate global performances of non-linear wavelet estimation in regression models with correlated errors. Convergence properties are studied over a wide range of Besov classes Bspi,r and for a variety of Lp error measures. We consider error distributions with Long-Range-Dependence parameter α, 0 < α ≤ 1. 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 s = α 2 ( p pi − 1) when p>