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Biometrika 1978 65(3):571-579; doi:10.1093/biomet/65.3.571
© 1978 by Biometrika Trust
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A robust analysis of the general linear model based on one step R-estimates

JOSEPH W. MCKEAN1 and THOMAS P. HETTMANSPERGER2

1Program of Mathematical Sciences, University of Texas Dallas
2Department of Statistics, Pennsylvania State University, University Park

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.

Key Words: Gauss-Newton • General linear hypotheses • Linear model • Regression • Robust estimation


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