Identification of influential observations on total least squares estimates (Q1601617)

Total least squares (TLS) solves for the unknown vector \(x\) in an overdetermined set of equations \[ Ax= b,\quad A\in\mathbb{R}^{m\times n},\quad b\in\mathbb{R}^{m\times 1},\quad m> n, \] where both the data matrix \(A\) and the data vector \(b\) are subject to errors. So the assumptions of TLS differ from those of ordinary least squares (OLS) where only \(b\) is subject to error. A major problem of the TLS technique is its higher sensitivity to outliers, or more generally, influential observations. The aim of the paper is to develop appropriate identification indices as diagnostic tools to identify the influential observations. The proposed methods are extensions of those for OLS. The paper contains two extensive numerical tests. The aim of the methods is not only to determine more reliable estimates of parameters but also to explore appropriate model structures. Indeed, outliers are not necessarily mis-recordings; their presence may be real and understanding them may help to improve the model.