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.