Regression Diagnostics for Rank-Based Methods

Abstract Residual plots and diagnostic techniques have become important tools in examining the least squares fit of a linear model. In this article we explore the properties of the residuals from a rank-based fit of the model. We present diagnostic techniques that detect outlying cases and cases that have an influential effect on the rank-based fit. We show that the residuals from this fit can be used to detect curvature not accounted for by the fitted model. Furthermore, our diagnostic techniques inherit the excellent efficiency properties of the rank-based fit over a wide class of error distributions, including asymmetric distributions. We illustrate these techniques with several examples.

[1]  Thomas P. Hettmansperger,et al.  A robust analysis of the general linear model based on one step R-estimates , 1978 .

[2]  Thomas P. Hettmansperger,et al.  Rank-based inference for linear models: asymmetric errors , 1989 .

[3]  Joseph W. McKean,et al.  A Robust Two-Stage Multiple Comparison Procedure with Application to a Random Drug Screen , 1989 .

[4]  T. A. Ryan,et al.  Algorithm 516: An Algorithm for Obtaining Confidence Intervals and Point Estimates Based on Ranks in the Two-Sample Location Problem [G1] , 1977, TOMS.

[5]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[6]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[7]  A. Afifi,et al.  Statistical Analysis: A Computer Oriented Approach , 1979 .

[8]  Hira L. Koul,et al.  An Estimator of the Scale Parameter for the Rank Analysis of Linear Models under General Score Functions , 1987 .

[9]  Louis A. Jaeckel.  Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals , 1972 .

[10]  Thomas P. Hettmansperger,et al.  Tests of hypotheses based on ranks in the general linear model , 1976 .

[11]  Siegfried Heiler,et al.  Asymptotic normality of r-estimates in the linear model , 1988 .

[12]  R. R. Hocking.  Developments in Linear Regression Methodology: 1959–l982 , 1983 .

[13]  J. McKean,et al.  The Geometry of Robust Procedures in Linear Models , 1980 .

[14]  Thomas P. Hettmansperger,et al.  A Geometric Interpretation of Inferences Based on Ranks in the Linear Model , 1983 .

[15]  Abdelmonem A. Afifi,et al.  Statistical Analysis: A Computer Oriented Approach. , 1973 .

[16]  Michael H. Kutner.  Applied Linear Statistical Models , 1974 .

[17]  Thomas P. Hettmansperger,et al.  A Robust Alternative Based on Ranks to Least Squares in Analyzing Linear Models , 1977 .

[18]  M. R. Osborne.  Finite Algorithms in Optimization and Data Analysis , 1985 .

[19]  S. Chatterjee.  Sensitivity analysis in linear regression , 1988 .

[20]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[21]  R. Dennis Cook,et al.  Regression Diagnostics With Dynamic Graphics , 1989 .

[22]  P. Hall,et al.  On the Distribution of a Studentized Quantile , 1988 .

[23]  Jack Dongarra,et al.  LINPACK Users' Guide , 1987 .

[24]  P. Sen,et al.  Nonparametric Methods in General Linear Models. , 1986 .

[25]  Joseph W. McKean,et al.  A comparison of methods for studentizing the sample median , 1984 .

[26]  Joseph W. McKean,et al.  Rank scores suitable for analyses of linear models under asymmetric error distributions , 1989 .