Abstract
Most algorithms for estimating high breakdown regression estimators in linear regression rely on finding the least squares fit to many p-point elemental sets, where p is the dimension of the X matrix. Such an approach is computationally infeasible in nonlinear regression. This article presents a new algorithm for computing high breakdown estimates in nonlinear regression that requires only a small number of least squares fits to p points. The algorithm is used to compute Rousseeuw's least median of squares (LMS) estimate and Yohai's MM estimate in both simulations and examples. It is also used to compute bootstrapped and Monte Carlo Standard error estimates for MM estimates, which are compared with asymptotic Standard errors (ASE's). Using the PROGRESS algorithm for a two-parameter nonlinear model with sample size 30 would require finding the least squares fit to 435 two-point subsets of the data. In the settings considered in this article, the proposed algorithm performs just as well with 25 as with 435 ...
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