The analysis of two-line like regression by means of LMS

Least median squares regression is widely considered very robust with respect to outliers on the basis of its very high breakpoint point of 50% (i.e. half of the data points considered can be outliers). But, there are some data configurations like that of the two-line regression problem for which the estimation of regression coefficients θ becomes very sensitive to small perturbations of the data set. We will analyze some of these data configurations and show how LMS regression, if extended to the set of the best local minimums of med r 2 (θ) when computing the LMS, becomes an effective method of analysis.