  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), Mat\'ern, 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.
