Using linear smoothers to assess the structural dimension of regressions
Using linear smoothers to assess the structural dimension of regressions
复制标题
使用线性平滑器评估回归的结构维度
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
E. Bura
中科院分区：
文献类型：
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作者：
E. Bura
切片逆回归（Li（1991））是一种简单的非参数估计方法，用于回归的结构维数，即由多维回归向量 X 的投影所跨越的线性子空间的维数，该向量包含有关随机变量 Y 对 X 的回归的部分或全部建模信息。在本文中，非参数估计方法扩展到包括线性平滑器系列。除了线性条件和二阶矩的存在之外，对回归量的分布没有任何限制。获得维度的渐近卡方检验。通过小型比较模拟研究来说明理论结果。
Sliced Inverse Regression (Li (1991)) is a simple nonparametric estima- tion method for the structural dimension of a regression, that is, for the dimension of the linear subspace spanned by projections of the multidimensional regressor vec- tor X that contains part or all of the modelling information about the regression of a random variable Y on X. In this paper, the nonparametric estimation method is extended to include the family of linear smoothers. No restrictions are placed on the distribution of the regressors except for the linearity condition and exis- tence of second moments. An asymptotic chi-square test for dimension is obtained. Theoretical results are illustrated with a small comparative simulation study.