论文标题
小波收缩的不对称先验
Asymmetric prior in wavelet shrinkage
论文作者
论文摘要
在贝叶斯小波的收缩中，假定已经提出的针对小波系数的先验是在零左右的对称性。尽管此假设在许多应用中都是合理的，但这并不是一般性的。本文提出了基于零点质量函数的离散混合物和在非参数回归模型中小波系数之前的不对称收缩规则。提供了统计特性，例如偏见，方差，经典和贝叶斯对相关的不对称规则的风险，并在涉及人工不对称分布系数和Donoho-Johnstone测试功能的模拟研究中获得了拟议规则的性能。还分析了地震真实数据集中的应用。
In bayesian wavelet shrinkage, the already proposed priors to wavelet coefficients are assumed to be symmetric around zero. Although this assumption is reasonable in many applications, it is not general. The present paper proposes the use of an asymmetric shrinkage rule based on the discrete mixture of a point mass function at zero and an asymmetric beta distribution as prior to the wavelet coefficients in a non-parametric regression model. Statistical properties such as bias, variance, classical and bayesian risks of the associated asymmetric rule are provided and performances of the proposed rule are obtained in simulation studies involving artificial asymmetric distributed coefficients and the Donoho-Johnstone test functions. Application in a seismic real dataset is also analyzed.
