  Re-scale boosting (RBoosting) is a variant of boosting which can essentially
improve the generalization performance of boosting learning. The key feature of
RBoosting lies in introducing a shrinkage degree to re-scale the ensemble
estimate in each gradient-descent step. Thus, the shrinkage degree determines
the performance of RBoosting.
  The aim of this paper is to develop a concrete analysis concerning how to
determine the shrinkage degree in $L_2$-RBoosting. We propose two feasible ways
to select the shrinkage degree. The first one is to parameterize the shrinkage
degree and the other one is to develope a data-driven approach of it. After
rigorously analyzing the importance of the shrinkage degree in $L_2$-RBoosting
learning, we compare the pros and cons of the proposed methods. We find that
although these approaches can reach the same learning rates, the structure of
the final estimate of the parameterized approach is better, which sometimes
yields a better generalization capability when the number of sample is finite.
With this, we recommend to parameterize the shrinkage degree of
$L_2$-RBoosting. To this end, we present an adaptive parameter-selection
strategy for shrinkage degree and verify its feasibility through both
theoretical analysis and numerical verification.
  The obtained results enhance the understanding of RBoosting and further give
guidance on how to use $L_2$-RBoosting for regression tasks.
