改进的多元线性回归模型及其应用

Improved multiple linear regression model and its applications

从EIV(Error-In-Variables)模型入手,对经典多元线性回归模型进行改进,并采用加权整体最小二乘估计准则(WTLS)对待估参数进行估计,最后针对新增观测信息的情况,导出其参数估值修正递推算法。通过建筑基坑支护桩水平位移监测实验表明,改进的模型较之经典模型能对水平位移变量进行更好的预测。参数修正递推算法的使用,避免了复杂的重复计算,计算效率明显提高。

h presents the improved multiple linear regression model whih is based on error-in-variablesmodel and then estimates the parameters by weighted total least squaIes. So it leads to the recursivealgorithm when new observations are available. The supporting piles hcrizontal displacement monitoringexperiments show the improved model is better than the classical model for predicting the horizontaldisplacement of the variable. The use of parameter correction recur,ive algorithm can avoid doublecounting of complex, and the computational efficiency has been improvec significantly.