Abstract
Publisher Summary This chapter discusses the rank tests for linear models. Gutenbrunner's research established an intimate link between the Hajek approach to linear rank statistics and the formulation of quantile regression appearing in Koenker and Bassett. The link is based on a formal linear programming duality between sorting and ranking and is the focus of the chapter. The chapter presents a unified perspective on the construction of rank tests for a broad spectrum of linear model applications. Statistical inference based on ranks continues to provide an extremely attractive alternative to classical, likelihood-based, inference methods. The approach to rank-based inference introduced by Gutenbrunner and Jureckova has significantly expanded the scope of these methods by providing an elegant generalization of the Hajek rankscore functions to linear models with nuisance parameters, thus circumventing alignment and preliminary estimation problems. Many interesting opportunities remain. The chapter focuses exclusively on hypotheses related to location and scale shift.
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