Hampel et al. Optimality requires that along the curves between and and between and , the value of is such that the ratio of the sensitivity of the variance to a change in the data over the asymptotic variance of the data is a constant. Indeed, the value of the ratio is . The value of fixes the threshold for the magnitude of beyond which an observation is completely rejected by assigning it a weight . The scale value remains unchanged but the weights are updated to match the current coefficient estimates.
Numerical convergence is required for both the values and the weights.
Because redescending -estimators such as the estimator have multiple solutions, starting values affect the results. We use to start the coefficients and use the LQD values for an initial set of residuals . Hampel et al.