超高维稀疏二次判别分析两阶段估计方法  

Two-stage Estimation Method for Ultra-high Dimensional Sparse Quadratic Discriminant Analysis

作　　者：高妍南 周生彬 黄叶金 白世贞[4] Gao Yannan;Zhou Shengbin;Huang Yejin;Bai Shizhen(College of Electronic and Information Engineering,Guangdong Ocean University;School of Information Engineering,Lingnan Normal University,Zhanjiang Guangdong 524048,China;China Securities Data Co.,Ltd.,Beijing 100032,China;Postdoctoral Station of Business Administration,Harbin University of Commerce,Harbin 150028,China)

机构地区：[1]广东海洋大学电子与信息工程学院 [2]岭南师范学院信息工程学院,广东湛江524048 [3]中证数据有限责任公司,北京100032 [4]哈尔滨商业大学工商管理博士后流动站,哈尔滨150028

出　　处：《统计与决策》2022年第6期9-14,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(71671054)。

摘　　要：文章提出一种两阶段二次判别分析建模方法,该方法将高维协方差阵的估计转化为低维矩阵的估计问题,从而有效解决了超高维二次判别分析计算量大的问题。数值模拟和实际数据分析结果表明,在有限样本情形下,两阶段估计方法在变量选择和分类误差率方面的性能更好。This paper proposes a modeling method for two-stage quadratic discriminant analysis, which transforms the estimation of high-dimensional covariance matrix into the estimation of low-dimensional matrix, thus effectively solving the problem of large computation of super-high-dimensional quadratic discriminant analysis. The results of numerical simulation and actual data analysis show that the two-stage estimation method has better performance in variable selection and classification error rate under finite samples.

关 键 词：二次判别分析 超高维 稀疏性 精度矩阵 两阶段估计 

分 类 号：O212.2[理学—概率论与数理统计]