增删数据场合最小二乘估计算法的比较研究

Comparative Research of LSE Algorithm under Additions and Deletions of Data

给出了增删数据场合多元线性回归模型参数最小二乘估计的两种算法—递推算法和Givens变换法,二者都利用已有的结果,减少计算量.递推算法给出预测误差的关系式,可直接比较预测误差大小;Givens变换法不能直接导出预测误差的关系式,但更容易算出残差平方和,可通过比较残差平方和大小比较增删数据前后参数估计的好坏.

This paper gives two algorithms for multiple linear regression model parameters LSE under additions and deletions of data-Recursive algorithm and Givens transform algorithm,then uses the result to educe the computational cost.Recursive algorithm gives the relation of prediction error,and can be directly compared.Givens transform algorithm can not be directly derived relation of prediction error,but more easily calculate residual sum of squares,and can be compared for the quality of parameter estimation under additions and deletions of data by residual sum of squares.