含高维相依自变量的中心k阶条件矩子空间的估计

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....

The Central Kth-Conditional Moment Suspace Estimation with Highly Dimensional and Highly Correlated Predictors

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