Sufficient Dimension Reduction under Dimension-reduction-based Imputation with Predictors Missing at Random
Sufficient Dimension Reduction under Dimension-reduction-based Imputation with Predictors Missing at Random
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DOI：
10.5705/ss.202017.0288
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发表时间：
2019
影响因子：
1.4
通讯作者：
Xiaojie Yang;Qihua Wang
中科院分区：
文献类型：
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作者：
Xiaojie Yang;Qihua Wang
在一些实际问题中，预测子的子集经常会丢失，特别是当预测子的维数很高时。对于这种情况，不能直接应用标准的充分降维（SDR）方法来避免维度灾难。本文提出了一种基于降维的插补方法，使得任何基于谱分解的SDR方法都适用于预测因子随机缺失的情况。切片逆回归（SIR）被用来说明这个过程。所提出的基于降维的SIR候选矩阵的插补估计量（称为DRI-SIR估计量）在某些温和的条件下是渐进正态的，因此所得的中心子空间估计量是根n相容的。通过仿真实验对该方法的有限样本性能进行了评估，并对一个真实的数据集进行了分析。Statistica Sinica：最新录用论文（录用版本以英文编辑为准）
In some practical problems, a subset of predictors are frequently subject to missingness, especially when the dimension of the predictors is high. For this case, the standard sufficient dimension reduction (SDR) methods cannot be applied directly to avoid the curse of dimensionality. A dimension-reductionbased imputation method is developed in this article such that any of spectraldecomposition-based SDR methods for full data is applicable to the case of predictors missing at random. The sliced inverse regression (SIR) is used to illustrate this procedure. The proposed dimension-reduction-based imputation estimator of the candidate matrix for SIR, termed as DRI-SIR estimator, is asymptotically normal under some mild conditions and hence the resulting estimator of the central subspace is root n consistent. The finite sample performance of the proposed method is evaluated through comprehensive simulations and a real data set is analyzed for illustration. Statistica Sinica: Newly accepted Paper (accepted version subject to English editing)