Estimation Of Parameters For The General Liner Error-in-covariance Model With Singular Covariance

The error-in-variable models can be used to solve the problem when the independent variables and the dependent variables all contain errors or maybe contain errors in the statistical field. This model has the very good application value in economy, military, forestry, and so on.In this paper, the general liner error-in-variable models are considered. The general model can be used to describe the linear relationship of variables in which some variables can be observed exactly, and others can not be observed exactly. In this kind of models, the general liner functional model, the general liner structure model and the general liner superstructure model are discussed here.The estimation of parameters of general linear error-in-covariance model with singular covariance is discussed, and the main works are as follows:1. Estimation of parameters for general liner functional model with singular covariance.First, the Rao decomposition of the sample variance and the known singular measure error variance are presented and then the square measure error with singular variance and the standardized condition are got. Furthermore that the square measure error is not depending on the choice of generalized matrix inverses is proved. Finally the least square estimation and the maximum likelihood estimation for this model are proposed.2. Estimation of parameters for the general liner structure models and the generalized liner superstructure models with singular covariance.In this paper the method of estimation of parameters for the general liner structure model is presented, and the corollary on the method of estimation of parameters for generalized liner superstructure model is proved.3. We give a simple numerical simulation, to test the effect of parameters estimation.