Estimation of errors-in-variables models

Abstract

The so-called errors-in-variables models pose serious problems to traditional statistical estimation because the Gaussian likelihood function, defined by the natural quadratic error measure, has a saddle point rather than a maximum. A discussion is presented of the estimation of such models, including the number of linear relations in them, based on the computation of a central concept in statistics: the stochastic complexity. In particular, an estimate of the linear relation between two such variables is demonstrated which has the property that when the level of the noise is reduced to zero, the estimate agrees with the correct solution.