This work proposes a Bayesian rule based on the mixture of a point mass function at zero and the logistic distribution to perform wavelet shrinkage in nonparametric regression models with stationary errors (with short or long-memory behavior). The proposal is assessed through Monte Carlo experiments and illustrated with real data. Simulation studies indicate that the precision of the estimates decreases as the amount of correlation increases. However, given a sample size and error correlated noise, the performance of the rule is almost the same while the signal-to-noise ratio decreases, compared to the performance of the rule under independent and identically distributed errors. Further, we find that the performance of the proposal is better than the standard soft thresholding rule with universal policy in most of the considered underlying functions, sample sizes and signal-to-noise ratios scenarios.

翻译：本文提出了一种基于零处点质量函数与Logistic分布混合的贝叶斯准则，用于对具有平稳误差（含短记忆或长记忆行为）的非参数回归模型进行小波收缩。通过蒙特卡洛实验对该方法进行了评估，并利用真实数据进行了验证。模拟研究表明，随着相关程度的增加，估计精度有所下降。然而，在给定样本量和误差相关噪声的情况下，与独立同分布误差下该准则的表现相比，当信噪比降低时，该准则的性能几乎保持不变。此外，我们发现在大多数考虑的本征函数、样本量和信噪比场景中，该准则的表现优于采用通用策略的标准软阈值规则。