| 一种基于加权F-范数的半正定矩阵的逼近方法 |
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| 引用本文： | 方建斌,陈正旭.一种基于加权F-范数的半正定矩阵的逼近方法[J].统计与信息论坛,2007,22(2):44-48. |
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| 作者姓名： | 方建斌 陈正旭 |
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| 作者单位： | 1. 江汉大学,数学与计算机科学学院,湖北,武汉,430056;武汉理工大学,理学院,湖北,武汉,430070
2. 武汉理工大学,理学院,湖北,武汉,430070 |
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| 摘 要： | 正定性是许多金融预测模型的重要假设前提，然而从实际样本中得到的相关系数矩阵并不能保证其正定性。为此在介绍如何根据样本设定相关系数矩阵以及范数逼近原理的基础上，如何根据该原理找到与之最接近的相关系数矩阵，即最接近的单位对角半正定对称矩阵。通过实证，验证了其方法的有效性。
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| 关 键 词： | 协方差矩阵 相关系数矩阵 矩阵逼近 F-范数 |
| 文章编号： | 1007-3116(2007)02-0044-05 |
| 修稿时间： | 2006年6月23日 |
An Approximation Method of Positive Semi-definite Matrix Based on Weighted F-norm |
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| FANG Jian-bin,CHEN Zheng-xu.An Approximation Method of Positive Semi-definite Matrix Based on Weighted F-norm[J].Statistics & Information Tribune,2007,22(2):44-48. |
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| Authors: | FANG Jian-bin CHEN Zheng-xu |
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| Institution: | FANG Jian-bin, CHEN Zheng-xu (1. School of Mathematics ＆ Computer Science, Jianghan University, Wuhan 430056, China; 2. School of Sciences, Wuhan University of Technology, Wuhan 430070, China) |
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| Abstract: | Positive is the important hypotheses of many financial forecasting models,but the correlation coefficient matrix we get from actual samples are not always positive.Firstly,we introduced how to set correlation coefficient matrix according to the sample,and introduced the theory of norm approximation,based on which we find the proximal correlation coefficient matrix,namely unit diagonal positive semi-definite symmetric matrix.Finally,the validity of method in this paper has been proved in practical experiment. |
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| Keywords: | covariance matrix correlation coefficient matrix matrix approximation F-norm |
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