Some new approaches to estimation in linear and nonlinear errors-in-variables regression models

Two recently proposed approaches to estimation in linear and nonlinear errors-invariables (EIV) regression models are reviewed. The first approach views the latent variables assumed to have a functional relationship as being random quantities, rather than fixed unknowns. In this case, the estimation problem can be reformulated as a classical nonlinear regression model, but with a regression function not always expressed in explicit form. The second approach is quite different, using simulation experiments to add known amounts of additional error variation to the measurements of the latent variables and thereby obtaining an empirical relation between ''naive'' least-squares estimates of the parameters and the amount of error variation present. Extrapolation of this estimator-variance relationship to the case where the error variation is zero yields the desired solution to the EIV regression problem.