Abstract
Hall et al. (1999) proposed block-thresholding methods to estimate mean regression functions with independent random errors. They showed that block-thresholded wavelet estimators attain minimax-optimal convergence rates when the mean functions belong to a large class of functions that involve a wide variety of irregularities, including chirp and Doppler functions, and functions with jump discontinuities. In this article, we show that block-thresholded wavelet estimators still attain minimax convergence rates when the mean functions belong to a wide range of Besov classes (where s > 1/p, p ≥ 1 and q ≥ 1) with long-memory Gaussian errors. Therefore, in the presence of long-memory Gaussian errors, wavelet estimators still provide extensive adaptivity.
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