Figure 1.

Visualization of the RR-BLUP estimator ($\left({\widehat{\mathbf{u}}}_{\text{RR}}\right)$) and the LASSO estimator ($\left({\widehat{\mathbf{u}}}_{\text{L}}\right)$) as solutions to a least-squares problem with different penalization [[38],[39]]. We illustrate a two-dimensional case. The blue ellipses show the contours of the RSS function around the ordinary least-square solution ($\left({\widehat{\mathbf{u}}}_{\text{OLS}}\right)$). The ridge estimator is the point at which the innermost elliptical contour touches the circular ridge penalty $\sqrt{u_1^2+u_2^2}<c_{\text{RR}}$. The LASSO estimator is the point at which the innermost elliptical contour touches the diamond shaped LASSO penalty |u₁| + |u₂|<c_L. Contrary to the ridge penalty, the LASSO penalty allows estimations to be exactly zero.