A hybrid bias correction algorithm for estimating straight line parameters

Abstract

In the common robust weighted total least squares estimator of the errors-in-variables model for straight line fitting, a bias exists in the estimated variance component used to reweight the weight matrix of observations when outliers are present. Additionally, when the second-order Taylor expansion of the functional model is not considered, the estimator is often computed with bias. A hybrid bias correction algorithm is proposed to reduce the two biases simultaneously and achieve unbiased results, which is demonstrated by three examples. The results show that the proposed algorithm can realize the bias correction of parameters and variance component estimated by robust weighted total least squares (RWTLS) ,and obtain the minimum variance component estimates. The new method is more suitable for correlation and/or outliers case and can detect outliers that cannot be detected by RWTLS.