7 Rank-based analyses of linear models

Abstract

Publisher Summary This chapter presents the rank-based analyses of linear models. These methods are based on robust estimates of regression parameters in the same way as the traditional analysis of variance (ANOVA) is based on least squares (LS) estimates. It also discusses two classes of robust estimates: regular R-estimates and generalized rank (GR)-estimates. The first class contains highly efficient estimates but their influence is only bounded in the Y space. The second class, although not as efficient, has bounded influence in both the Y and the X spaces. The chapter also presents the rank-based analysis for regular R-estimates and GR-estimates, respectively. The rank-based analysis offers the tests of general linear hypotheses and related inference procedures for all the models covered by the traditional ANOVA and analysis of covariance methods based on LS-estimates. These rank-based analyses are generalizations of the nonparametric procedures in the simple location problems. The rank-based analysis is a highly efficient, attractive alternative to the traditional least squares ANOVA and covariance. The coefficients of determination for both classes of estimates are discussed in the chapter. These are robust analogues of the popular R 2 statistic based on LS estimates.