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

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.

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 kth-conditional moment function.For this,we first borrow the new concept — the central kth-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 kth-moment weighted partial least squares to handle with the estimation of the central kth-conditional moment subspace.Finally,we obtain strong consistency.