EM algorithm for generalized Ridge regression with spatial covariates

Abstract

AbstractThe generalized Ridge penalty is a powerful tool for dealing with multicollinearity and high‐dimensionality in regression problems. 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 when the covariates are spatially correlated. 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.