A constructive approach to the estimation of dimension reduction directions
A constructive approach to the estimation of dimension reduction directions
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DOI：
10.1214/009053607000000352
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发表时间：
2007-12-01
影响因子：
4.5
通讯作者：
Xia, Yingcun
中科院分区：
文献类型：
--
作者：
Xia, Yingcun
在本文中，我们提出了两种新的方法来估计降维方向的中心子空间（CS）通过构建一个回归模型，使所有的方向都被捕获在回归均值。与逆回归估计方法[例如，J. Amer统计学家。Assoc.86（1991）328-332，J Amer Statistist. Assoc.86（1991）316-342，J Amer Statistist. Assoc.87（1992）1025-1039]，新方法不需要对协变量的设计或回归变量与响应变量之间的函数关系作强假设，并且在有限样本下比逆回归估计方法有更好的性能。与直接回归估计方法[例如，J.美国统计学家Assoc.84（1989）986-995，Ann. Statistist. 29（2001）1537-1566，J R. Stat. Soc. Ser B Stat.美沙酮64（2002）363-410]中提出的方法，该方法只能在回归均值中估计CS的方向，而新的方法可以穷尽地检测CS的方向。证明了估计量的相合性和相应算法的收敛性。
In this paper we propose two new methods to estimate the dimension-reduction directions of the central subspace (CS) by constructing a regression model such that the directions are all captured in the regression mean. Compared with the inverse regression estimation methods [e.g., J. Amer Statist. Assoc. 86 (1991) 328-332, J Amer Statist. Assoc. 86 (1991) 316-342, J Amer Statist. Assoc. 87 (1992) 1025-1039], the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable, and have better perforrnance than the inverse regression estimation methods for finite samples. Compared with the direct regression estimation methods [e.g., J. Amer. Statist. Assoc. 84 (1989) 986-995, Ann. Statist. 29 (2001) 1537-1566, J R. Stat. Soc. Ser B Stat. Methodol. 64 (2002) 363-410], which can only estimate the directions of CS in the regression mean, the new methods can detect the directions of CS exhaustively. Consistency of the estimators and the convergence of corresponding algorithms are proved.