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.

在本文中，我们考虑具有负超加性相依（NSD）误差的异方差非参数模型中的回归函数，考虑了两个估计器：硬阈值小波估计器和块阈值小波估计器。随机设计分布是已知的还是未知的，并且对于\（{L ^ 2} \），在Besov空间上研究了这些估计量的相应自适应属性。风险。结果表明，块阈值估计器在理论上和计算上均优于硬阈值估计器，前者可达到最佳收敛速度，而后者可达到近乎最佳收敛速度。因此，即使存在异方差NSD错误，块阈值估计器仍可对许多不规则函数类别提供广泛的适应性。