Polynomial regression modeling based on Gram-Schmidt process
-
摘要: 多项式回归模型是一种常用的非线性回归方法.由于在多项式回归模型中,自变量之间往往存在较强的相关关系,采用普通最小二乘回归方法来估计回归系数会存在较大的计算误差.为了提高多项式回归模型的预测准确性和可靠性,提出一种基于Gram-Schmidt过程进行多项式回归的建模方法,可以实现自变量集合的正交化,克服自变量集合多重共线对回归建模的不良影响,从而有效地运用最小二乘建立回归模型.同时可以进行信息筛选有效选取对因变量有显著解释作用的自变量,排除自变量中的冗余信息.采用仿真数据分析,检验了该方法的有效性.
-
关键词:
- Gram-Schmidt过程 /
- 多项式回归 /
- 多重相关性
Abstract: The polynomial regression model is a widely applied nonlinear regression method. Since the high correlation exists among independent variables in the polynomial regression model, it will induce excessive computational error to estimate coefficients with the ordinary least square regression. A method of polynomial regression modeling based on Gram-Schmidt process which can achieve the orthogonalization of the independent variables and overcome the adverse effects of multicollinearity to regression modeling was proposed, so as to apply ordinary least square to regression modeling effectively. The independent variables including notable explaining information can be selected effectively, at the same time redundant information is deleted. Simulation data analysis was adopted to test the effectiveness of the method.-
Key words:
- Gram-Schmidt process /
- polynomial regression /
- multiple correlation
-
[1] Wold S,Martens H,Wold H．The multivariate calibration problem in chemistry solved by the PLS method[M]． Heidelberg: Springer-Verlag, 1983 [2] Tenenhaus M． L’approche PLS[M]． Revue de Statistique Appliquée, 1998 [3] 王惠文．偏最小二乘回归方法及其应用[M]．北京:国防工业出版社, 1999:93-107 Wang Huiwen． Partial least-squaresregression-method and applications[M]． Beijing: National Defense Industry Press,1997,93-107(in Chinese) [4] 付凌晖,王惠文．多项式回归的建模方法比较研究[J]．数理统计与管理, 2004, 23(1): 48-52 Fu Linghui,Wang Huiwen． A comparative reseach of polynomial regression modelling methods[J]．Application of Statistics and Management, 2004, 23(1): 48-52(in Chinese) [5] Jain S K,Gunawarddena A D．Linear algebra: an interactive approach[M]． Bejing:China Machine Press,2003 [6] 内特,沃塞曼,库特纳． 应用线性回归模型[M].张勇,王国明,赵秀珍译． 北京:中国统计出版社, 1990 Neter,Wasserman,Kutner． Applied linear regression model[M]． Translated by Zhang Yong, Wang Guoming,Zhao Xiuzhen．Beijing:China Statistics Press,1990(in Chinese) [7] 王惠文,陈梅玲,Gilbert Saporta． Gram-Schmidt回归及在刀具磨损预报中的应用[J]．北京航空航天大学学报,2008,34(6): 729-733 Wang Huiwen,Chen Meiling,Gilbert Saporta．Gram-Schmidt regression and application in cutting tool abrasion prediction[J]．Journal of Beijing University of Aeronautics and Astronautics,2008,34(6): 729-733(in Chinese) -
点击查看大图
计量
- 文章访问数: 3043
- HTML全文浏览量: 224
- PDF下载量: 1330
- 被引次数: 0
下载:
