回归分析中的目标函数极小化准则

指出了最小二乘回归分析中存在稳健性不好的问题，讨论了用线性规划法计算回归系数的最小一乘准则和极小极大化准则，通过实例计算得出最小一乘准则误差绝对值小，最大误差最大和极小极大化准则误差绝对值之和最大，最大误差最小的结果，指出在实际应用中可以把三种准则下的计算结果进行比较，从中选出最优回归方程。

Research on the Objective Function Minimization Standards in the Regression Analysis

This paper points out an instability factor in the least double linear regression analysis and discusses the calculation of the least linear standards of regression coefficient and minimax standards by employing the linear programming method. As proved by the practical examples, the sum of criterion absolute values of the least linear standards is minimum and the maximum criterion is maximum, etc.. The paper highlights the possible selection of the optimal regression function by comparing the results derived from the three standards depending on the practical application.