Sufficient dimension reduction, replacing the original predictors with a few linear combinations while keeping all the regression information, has been widely studied. A key goal is to find the central mean subspace, the intersection of all subspaces that provide such a reduction. To this end, a new sufficient dimension reduction method is proposed, with two estimation procedures, through a novel approach of feature filter, applicable to both univariate and multivariate responses. Asymptotic results are established. Estimation methods to determine the structural dimension, to obtain sparse estimator and to deal with large p small n data are provided. The efficacy of the method is demonstrated by simulations and a real data example.

充分降维，在保留所有回归信息的同时，用几个线性组合代替原始预测变量，已被广泛研究。一个关键目标是找到中心平均子空间，即提供这种减少的所有子空间的交集。为此，提出了一种新的充分降维方法，它具有两个估计程序，通过一种新的特征滤波器方法，适用于单变量和多变量响应。渐近结果成立。提供了确定结构维数、获得稀疏估计量和处理大p小n数据的估计方法。该方法的有效性通过模拟和真实数据示例得到证明。