线性回归模型的稳健总体最小二乘解算

针对线性回归中自变量和因变量可能含有粗差的情况，提出线性回归模型的稳健总体最小二乘法。将线性回归模型进行等价变换，视其总体最小二乘平差模型为非线性，根据选权迭代的思想推导线性回归模型的稳健总体最小二乘迭代算法。以模拟算例在自变量和因变量同时添加粗差的情况下进行10 000次试验，并从中选出一组数据进行具体分析，结果验证了本文算法的有效性和可行性。

The Solution of Robust Total Least Squares for Linear Regression Models

Aiming at the situation that there are gross errors in the independent variable and dependent variable of the linear regression model，we propose the robust total least squares method.On the basis of the nonlinear adjustment model, we have deduced robust total least squares estimation calculation formula with selecting weight iteration through the equivalence transformation of the linear regression model. Finally, we apply the method to an example, and verify the feasibilities of the method.