Fig. 2.

Illustration of the robust-ODAL method. I: Using data from Site 1 (i.e., local site) to estimate the local estimator $\overline{\beta }$, and transfer $\overline{\beta }$ to other sites. II: Intermediate term $\nabla L_j(\overline{\beta })$ is evaluated at each site and transfer back to Site 1. III: With $\nabla L_1(\overline{\beta })$ and L₁(β), we obtain the surrogate function $\widetilde{L^R}(\beta )$ and the robust-ODAL estimator $\tilde{\beta }$ is obtained by maximizing the surrogate function (4).