摘要
针对传统最小二乘估计法忽略多元线性回归模型设计矩阵部分元素受误差影响的问题,提出采用结构整体最小二乘法估计模型参数,该方法同时考虑设计矩阵的误差和结构特性,以及与观测矢量异方差的情况。定义了结构整体最小二乘法估计模型参数的函数模型和随机模型,采用拉格朗日乘数法推导了其迭代解算的公式,并设计了相应的迭代算法。最后,通过模拟数据和建筑工程造价实测数据实验对算法的可行性和优越性进行了验证。
This paper presents the structured total least squares method for multivariable linear regression model with applications in engineering cost prediction. Following the mixed least squares-total least squares method in which the fixed columns of the design matrix is taken into account,the structured total least squares method is derived for a more generic case in which the heteroscedasticity is considered between independent variable and dependent variable. The solution formulas derived by Lagrange multiply method. According to these formulas,an iterative algorithm is suggested,and is validated by two numerical experiments at last.
出处
《四川建筑科学研究》
北大核心
2016年第4期142-147,共6页
Sichuan Building Science
基金
高等职业技术教育研究会研究项目(GZYLX2015072)
关键词
工程造价
多元线性回归模型
结构整体最小二乘法
预测
engineering cost
multivariable linear regression model
structured total least squares
prediction
