总体最小二乘回归预测模型的方差分量估计

回归预测模型是对传统回归模型的进一步扩展,不仅涉及回归模型的固定参数估计,而且将模型预测纳入平差的部分内容,更加符合实际解算需求。针对在回归模型预测中经常出现待预测非公共点(自变量)含有观测误差和随机模型不准确的问题,基于EIV(errors-in-variables)模型提出了一种同时顾及所有变量观测误差的整体解法。同时,将方差-协方差分量估计方法引入回归预测模型解算中,以修正随机模型与待预测非公共点的先验协因数阵,并推导了相关计算公式和迭代算法。算例试验表明,该方法能够有效估计各类观测数据的方差分量,为获取更合理的参数估计与更高的模型预测精度提供了可行手段。另外,通过设计多种对比方案可知,该方法的预测效果较好,尤其是针对观测数据与系数矩阵中随机元素之间存在一定相关性的情况。

Variance Components Estimation for Total Least-Squares Regression Prediction Model

As a further extension of traditional regression model, the regression prediction model not only involves the fixed parameter estimation of regression model, but also incorporates the model prediction into part of adjustment, which is more in line with the solutions of actual requirements. Focusing on the issues of predicted non-common points(independent variables) polluted with errors and inaccurate stochastic model,this paper proposes a new complete solution with a sufficient consideration to all errors of each variables based on errors-in-variables(EIV) model. Meanwhile, performed with the methodology of variance-covariance component estimation, stochastic model and prior cofactor matrix of the predicted non-common points have been corrected. The corresponding formulas are derived and the iterative algorithm is also presented. Experimental design shows that the presented approach can effectively achieve the estimation of variance components for various types of observations. It provides a feasible means for retrieving more reasonable parameter results and achieving higher prediction accuracy. In addition, the prediction effect of our presented approach is better over other control schemes, especially for the situation where there is a certain correlation between the observed data and the random elements in coefficient matrix.