Identification of influential observations on total least squares estimates

Abstract

It is known that total least squares (TLS) estimates are very sensitive to outliers. Therefore, identification of outliers is important for exploring appropriate model structures and determining reliable TLS estimates of parameters. In this paper, we investigate sensitivities of TLS estimates as observation data are perturbed, and then, based on perturbation theory of matrices, we develop identification indices for detecting observations that highly influence the TLS estimates. Finally, numerical examples are given to illustrate the proposed detection method.