On cross-distance selection algorithm for hybrid sufficient dimension reduction

Given the extensive development of a variety of sufficient dimension reduction (SDR) methodologies, Ye and Weiss (2003) proposed a hybrid SDR method combining two pre-existing SDR methods. In particular, they used a bootstrap approach to select a proper weight. Since bootstrapping is computationally intensive and time-consuming, the hybrid reduction approach has not been widely used, although it is more accurate than conventional single SDR methods. To overcome these deficits, we propose a novel cross-distance selection algorithm. Similar to the bootstrapping method, the proposed selection algorithm is data-driven and has a strong rationale for its performance. The numerical studies demonstrate that the chosen hybrid method from our proposed algorithm offers a good estimation quality and reduces the computing time dramatically at the same time. Furthermore, our real data analysis confirms that the proposed selection algorithm has potential advantages with its practical usefulness over the existing bootstrapping method.