EM algorithm for generalized Ridge regression with spatial covariates
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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.
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