Nonlinear total least-squares variance component estimation for GM(1,1) model

Abstract

The solution of the grey model (GM(1,1) model) generally involves equal-precision observations, and the (co)variance matrix is established from the prior information. However, the data are generally available with unequal-precision measurements in reality. To deal with the errors of all observations for GM(1,1) model with errors-in-variables (EIV) structure, we exploit the total least-squares (TLS) algorithm to estimate the parameters of GM(1,1) model in this paper. Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation, we further present a nonlinear total least-squares variance component estimation approach for GM(1,1) model, which resorts to the minimum norm quadratic unbiased estimation (MINQUE). The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

Keywords

• GM(1,1) model
• Minimum norm quadratic unbiased estimation (MINQUE)
• Total least-squares (TLS)
• Unequal-precision measurement
• Variance component estimation (VCE)