ROBUST AND HIGH-BREAKDOWN FITS OF POLYNOMIAL-MODELS

A common strategy for fitting a polynomial regression model is to use a combination of residual plots and significance tests on the regressi on coefficients. In this article, we consider whether this strategy ca n be used effectively for fits based on two classes of robust estimate s-namely, M estimates and GM estimates. We show that the asymptotic re lative efficiency of Mallows-type high-breakdown GM estimates can be q uite low for detecting curvature in polynomial models. Furthermore, th e GM-residual plots may also be of little help in detecting curvature. An example and a simulation study illustrate the discussion.