Total Least Squares Approach in Regression Methods

Total least squares (TLS) is a data modelling technique which can be used for many types of statistical analysis, e.g. a regression. In the regression setup, both dependent and independent variables are considered to be measured with errors. Thereby, the TLS approach in statistics is sometimes called an errors-invariables (EIV) modelling and, moreover, this type of regression is usually known as an orthogonal regression. We take an EIV regression model into account. Necessary algebraic tools are introduced in order to construct the TLS estimator. A comparison with the classical ordinary least squares estimator is illustrated. Consequently, the existence and uniqueness of the TLS estimator are discussed. Finally, we show the large sample properties of the TLS estimator, i.e. a strong and weak consistency, and an asymptotic distribution.