含高维相依自变量的中心k阶条件矩子空间的估计
The Central kth-Conditional Moment Suspace Estimation with Highly Dimensional and Highly Correlated Predictors
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摘要: 在回归分析中往往对条件均值, 条件方差及高阶条件矩特别感兴趣. 本文我们将关注中心k阶条件矩子空间在高维相依自变量情形的估计问题. 为此, 我们首先引入中心k阶条件矩子空间的概念, 并研究该子空间的基本性质. 针对高维相依自变量的复杂数据, 为了避免预测变量协方差阵的逆矩阵的计算, 本文提出用偏最小二乘方法来估计中心k阶条件矩子空间. 最后得到了估计的强相合性等渐近性质.
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关键词:
- 充分降维子空间 /
- 中心k阶条件矩子空间 /
- 高维相依 /
- 最小二乘估计 /
- 偏最小二乘
Abstract: The conditional mean, variance and higher-conditional moment functions are often of special interest in regression. In this paper,we generalize central mean subspace and focus especial attention on the k th-conditional moment function. For this, we first borrow the new concept --- the central k th-conditional moment subspace, and study its basic properties. To avoid computing the inverse of the covariance of predictors with large dimensionality and highly collinearity, we develop a method called the $k$th-moment weighted partial least squares to handle with the estimation of the central k th-conditional moment subspace. Finally, we obtain strong consistency -
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