A robust analysis of the general linear model based on one step R-estimates

Classical analysis of variance with least squares fitting is often used to discern structure in a linear model. McKean & Hettmansperger (1976) proposed a robust analysis based on ranks using the R-estimates proposed by Jaeckel (1972). These rank procedures depend on minimizing a dispersion surface and as a result are computationally restricted to small to moderate sized sets. In this paper we propose one step iterations based on a second derivative approximation to the surface. These estimates can be obtained quickly from initial estimates. Further the analysis resulting from these estimates is asymptotically equivalent to the minimum dispersion analysis. Thus it can be recommended for large data sets.