Total Robustified Least Squares Estimation in Partial Errors-in-variables Model

The weighted total least-squares (WTLS) estimate for the partial errors-in-variables (EIV) model is very susceptible to outliers. Because the observations and coefficient matrix in the partial EIV model may be contaminated with outliers simultaneously, a total robustified least squares (TRLS) estimation for the partial EIV model is proposed by combining a two-step iterated algorithm of the WTLS estimate with the equivalent weight method of robust M-estimation. And the uniformly most powerful test statistics are constructed to determine the down-weighting factors. For the characteristics of the two-step iterated method, two different down-weighting schemes are presented. In the first scheme down-weighting is only implemented for the coefficient matrix and not for the observations when some elements of the coefficient matrix are estimated, and the second scheme is contrary. A simulated two-dimensional affine transformation and a linear fitting with real data are analyzed. The results show that the TRLS with the first scheme is superior to one with the second scheme, and it outperforms the existing robust methods with residual and posterior estimate of variance of unit weight and existing robust methods for the general EIV model.