Iteratively reweighted total least squares for PEIV model

Abstract

The weighted total least-squares (WTLS) estimate for the partial EIV (PEIV) model is very susceptible to outliers. In view of outliers in observations and coefficient matrix, a robust estimate of WTLS which makes using of iteratively reweighted technique (IRTLS) for the PEIV model is developed by combining a new two-step iterated algorithm of the WTLS estimate with the sensitivity-analysis based on the robust M-estimation. The uniformly most powerful test statistics are constructed to determine the down-weighting factor and the variance of unit weight is estimated by least median squares (LMS) method possessing high break-down point. Depended on the PEIV model, two different down-weighting schemes are presented. In the first scheme down-weighting is only implemented for the coefficient matrix and not for observations when the elements of the coefficient matrix are estimated, and the second scheme is contrary. The most attractive aspect is that the suggested computational formulae are the same with the traditional robust least-squares (LS) methods. The two-dimensional affine transformation and liner fitting example are analyzed, and some comparisons are performed with different available weight functions. The proposed approach (Scheme 1) proves to be a powerful tool in detecting outliers for the PEIV model.