ABSTRACT
This chapter discusses the application of redescending M-estimators to the problem of multiple solutions. Regression is not only a methodology for fitting preconceived equations to data which follow the model quite closely. It is also a tool for data description. Regression diagnostics and bounded-influence regression both address this problem to a limited degree. A regression estimator with a high breakdown point is the ideal first step in the search for multiple answers. The value to which the successive estimates converge depends on the starting estimate. One way in which two regression surfaces can appear is through peculiarities in a design, either if the true surface is curved or if the error distribution has heavy tails. A helpful graphical device is to plot the eigenvectors associated with the two largest eigenvalues of the design covariance matrix against each other.
