This work proposes a wavelet shrinkage rule under asymmetric LINEX loss function and a mixture of a point mass function at zero and the logistic distribution as prior distribution to the wavelet coefficients in a nonparametric regression model with gaussian error. Underestimation of a significant wavelet coefficient can lead to a bad detection of features of the unknown function such as peaks, discontinuities and oscillations. It can also occur under asymmetrically distributed wavelet coefficients. Thus the proposed rule is suitable when overestimation and underestimation have asymmetric losses. Statistical properties of the rule such as squared bias, variance, frequentist and bayesian risks are obtained. Simulation studies are conducted to evaluate the performance of the rule against standard methods and an application in a real dataset involving infrared spectra is provided.

翻译：本文提出了一种在非对称LINEX损失函数下的贝叶斯小波收缩规则，该规则以零点处的点质量函数与逻辑斯谛分布的混合作为高斯误差非参数回归模型中小波系数的先验分布。对显著小波系数的低估可能导致对未知函数特征（如峰值、不连续点和振荡）的检测不良，这种情况也可能出现在非对称分布的小波系数中。因此，当过高估计和过低估计具有非对称损失时，所提出的规则尤为适用。本文推导了该规则的统计性质，包括平方偏差、方差、频率学派风险与贝叶斯风险。通过仿真研究评估了该规则相对于标准方法的性能，并提供了其在红外光谱真实数据集中的应用实例。