Algebraic relationships between classical regression and total least- squares estimation (Q1094861)

The classical linear regression model \(y=X\beta +\epsilon\) can be extended to a linear errors-in-variables model which considers all observations X, y subject to measurement errors. For these problems, the total least-squares (TLS) approach yields strongly consistent estimators. The authors derive some algebraic equivalences and relationships between classical estimators and TLS in the presence of collinearities.