A new approach to the variable selection using the TLS approach

The problem of variable selection is one of the most pervasive model selection problems in statistical applications. It arises when one wants to explain the observations or data adequately by a subset of possible regression variables. The objective is to identify factors of importance and to include only variables that contribute significantly to the reduction of the prediction error. Numerous selection procedures have been proposed in the classical multiple linear regression model. We extend one of the most popular methods developed in this context, the backward selection procedure, to a more general class of models. In the basic linear regression model, errors are present on the observations only, if errors are present on the regressors as well, one gets the errors-in-variables model which for Gaussian noise becomes the total-least-squares model, this is the context considered here.