The adaptivity of thresholding wavelet estimators in heteroscedastic nonparametric model with negatively super-additive dependent errors

Abstract

In this paper, we consider two estimators, a hard thresholding wavelet estimator and a block thresholding wavelet estimator, for the regression function in heteroscedastic nonparametric model with negatively super-additive dependent (NSD) errors. The random design distribution is known or unknown, and the corresponding adaptive properties of these estimators are investigated over Besov spaces, for the $${L^2}$$ risk. The results indicate that the block thresholding estimator is theoretically and computationally superior to the hard thresholding estimator with the former attains the optimal convergence rates, while the later achieves the nearly optimal convergence rates. Thus the block thresholding estimator provides extensive adaptivity to many irregular function classes even though with the presence of heteroscedastic NSD errors.