引入拉格朗日算子的最佳线性回归模型选择

基于同时考虑自变量和因变量测量误差的线性回归模型，首先将众多待选模型统一为附有约束条件的线性回归模型，然后采用含有多个备选假设的假设检验理论，并以拉格朗日算子构造假设检验统计量，提出最佳线性回归模型选择方法。实验结果表明，该算法可以获得符合观测数据实际的最佳线性回归模型，而且较改进后的线性假设法更简便。

Optimum Linear Regression Model Selection Algorithm with Lagrange Multipliers

On the basis of linear regression model, considering the measurement errors of independent variables and dependent variables at the same time, this paper first unifies many models to be selected into the linear regression model with constraints, adopts the hypothesis testing theory with multiple alternative hypotheses, and then constructs the hypothesis testing statistics with Lagrange multipliers. We propose the optimum selection algorithm of the linear regression model. The experimental results show that the proposed algorithm can obtain the optimum linear regression model, which is in accordance with actual observations and simpler than the improved linear hypothesis method.