A covariance structure analysis approach to the errors-in-variables estimation problem

It is a well-known fact that standard regression techniques, when applied to errors-in-variables (EIV) models, lead to biased and inconsistent parameter estimation. The work presented in this thesis address the EIV estimation problem using covariance structure analysis (CSA). When performing CSA, the standard implementation of the minimum distance (MD) estimator is to apply computationally demanding nonlinear least squares (NLLS). This thesis provides a solution to this problem by proposing a computationally less demanding separable nonlinear least squares (SNLLS) implementation of the estimator. The thesis consists of four papers. The first paper presents a covariance matching (CM) approach for identifying the single-input single-output (SISO) EIV model. The outlined approach extends previous known results by deriving an asymptotic covariance matrix of the jointly estimated system parameters, noise variances and auxiliary parameters. The second paper introduces two formulations of the SISO EIV model using structural equation modeling (SEM). The two formulations allow for quick implementation using standard SEM-based software. The third paper propose a numerically more efficient implementation of the MD estimator for estimating confirmatory factor analysis (CFA) models. The implementation uses an SNLLS approach, which allows part of the parameter vector to be estimated using numerically efficient linear techniques. The fourth and final paper presents a CFA-EIV modeling approach that allows for colored output noise. The presentation extends previous work by including a detailed treatment of the theoretical aspects of the MD estimator. All four papers use simulation examples to illustrate the outlined procedures.