| 摘要: |
| 本文提出两种基于迭代海森变换的多元响应变量降维方法: 1. 应用主成分分析方法对$q$维响应变量$\textbf{\textit{Y}}$降维, 由加权的迭代海森变换核矩阵估计中心均值子空间; 2. 构造$\textbf{\textit{Y}}$的特征函数的傅里叶变换, 通过迭代海森变换估计多元响应变量$\textbf{\textit{Y}}$的中心降维子空间. 建立了中心均值子空间估计的一致性. 数据模拟和实数据分析验证了所提方法的有效性. |
| 关键词: 迭代海森变换 中心均值子空间 主成分分析 矩母函数 充分降维 |
| DOI： |
| 分类号:O212.4 |
| 基金项目:山西省自然科学基金资助项目(RD2200002021) |
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| A STUDY ON SUFFICIENT DIMENSION REDUCTION ALGORITHMS FOR MULTIVARIATE RESPONSE VARIABLES |
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shenliangliang, zhangjunying
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School of Mathematics, Taiyuan University of Techology
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| Abstract: |
| This paper proposes two dimension reduction methods for multivariate response variables based on the Iterative Hessian Transformation:
(1) the first method performs principal component analysis on the $q$-dimensional response variable $\textbf{\textit{Y}}$, and estimates the central mean subspace using a weighted Iterative Hessian Transformation kernel matrix;
(2) the second method constructs the Fourier transform of the characteristic function of $\textbf{\textit{Y}}$, and estimates the central subspace via the Iterative Hessian Transformation framework.
The consistency of the central mean subspace estimator is established.
Simulation studies and real data analysis demonstrate the effectiveness of the proposed methods. |
| Key words: Iterative Hession Transformation central mean subspace principal component analysis moment generating function Sufficient Dimension Reduction |
