论文标题
使用空间协变量的广义山脊回归的EM算法
EM algorithm for generalized Ridge regression with spatial covariates
论文作者
论文摘要
普遍的山脊惩罚是处理过度拟合和高维回归的强大工具。广义脊回归可以作为具有正常先验和给定协方差矩阵的后验分布的平均值。协方差矩阵控制了系数的结构，这取决于特定应用。例如，假设系数在空间应用中具有空间结构是适当的。这项研究提出了一种预期最大化算法，用于估计其协方差结构取决于特定参数的广义脊参数。我们专注于三种情况：对角线（当协方差矩阵为对角线具有恒定元素），Matérn和有条件的自回旋协方差。进行了仿真研究以评估所提出的方法的性能，然后应用该方法用于使用风条件进行预测海浪高度。
The generalized Ridge penalty is a powerful tool for dealing with overfitting and for high-dimensional regressions. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given covariance matrix. The covariance matrix controls the structure of the coefficients, which depends on the particular application. For example, it is appropriate to assume that the coefficients have a spatial structure in spatial applications. This study proposes an expectation-maximization algorithm for estimating generalized Ridge parameters whose covariance structure depends on specific parameters. We focus on three cases: diagonal (when the covariance matrix is diagonal with constant elements), Matérn, and conditional autoregressive covariances. A simulation study is conducted to evaluate the performance of the proposed method, and then the method is applied to predict ocean wave heights using wind conditions.
