标题： 基于Epanechnikov核的低信噪比数据的贝叶斯小波收缩 显示英文标题

标题： Bayesian wavelet shrinkage for low SNR data based on the Epanechnikov kernel

摘要： 考虑具有加性高斯噪声的单变量非参数回归模型，并以小波基表示未知回归函数。 我们提出了一种收缩规则，通过将零点质量函数与Epanechnikov分布混合作为系数的先验来估计小波系数。 该规则被证明适用于低信噪比数据集的场景，并在模拟研究中优于标准方法和贝叶斯方法。 提供了平方偏差和方差等统计特性，并得到了该规则的显式表达式。 使用真实EEG数据集展示了该规则的应用。 显示英文摘要

摘要： Consider the univariate nonparametric regression model with additive Gaussian noise and the representation of the unknown regression function in terms of a wavelet basis. We propose a shrinkage rule to estimate the wavelet coefficients obtained by mixing a point mass function at zero with the Epanechnikov distribution as a prior for the coefficients. The proposed rule proved to be suitable for application in scenarios with low signal-to-noise ratio datasets and outperformed standard and Bayesian methods in simulation studies. Statistical properties, such as squared bias and variance, are provided, and an explicit expression of the rule is obtained. An application of the rule is demonstrated using a real EEG dataset.