一类多元响应降维子空间的估计及其应用

A Class of Estimators and Their Modified Versions for Dimension Reduction Subspace with Multivariate Responses and Its Application

在高维空间中进行统计建模通常会碰到"维数祸根"问题,解决办法之一是降维,充分降维是一种有效的降维方法。针对多维响应降维子空间提出一类矩生成函数估计方法及其改进估计量,并给出该类方法估计量的大样本性质:相合性、渐近正态性。通过随机模拟与实例分析,表明改进估计量估计效果有较大幅度提高。

Curse of dimensionality may happen when statistical modeling in high dimensional space,one approach to these problems is dimension reduction,sufficient dimension reduction is efficient for that.A class of estimators and their modified versions based on moment-generating function to estimate the central dimensional reduction subspace with multivariate responses are proposed,their large number property is given,that is consisigency and asymptotic property of estimators,finally statistical simulations and theirs application show that the modified versions are better than the old.