On a consistent rank estimate in a linear structural model

Abstract

The structural linear model is considered that is an errors-invariables
model where the unobserved variables are i.i.d. In this model we can find
linear transformations depending on the parameter, such that the transformed
observations using the true parameter are uncorrelated. Then an estimator is defined
as a zero point of a consistent correlation estimator. The Pearson estimate of the
covariance delivers the total least squares estimate. A rank estimation is proposed
as a zero point of Kendalls correlation measure and its consistency is shown.