Chapter 10 - Miscellaneous topics in regression rank tests

Abstract

This chapter presents miscellaneous topics in regression rank tests. The theory of rank tests pertains to a null hypothesis of invariance, against suitable alternatives. In a relatively more general set up, a null hypothesis, because of the presence of some nuisance parameter, may be composite, and in that way, lacking invariance, tile natural appeal and simplicity of the classical rank tests may no longer be tenable. The ranking after alignment principle for the randomized block design provides an alternative avenue for interblock comparisons and, thereby enhancing the information contained in the rankings. This generally leads to a more efficient testing procedure, though often resulting in only being conditionally distribution free. The intrablock rank tests are based on the within-block ranks and have been characterized as EDF. The alignment principle works out well in all asymptotic set up, and in this context the asymptotic linearity of linear rank statistics in the regression parameter plays a key role. It is found that regression quantiles (RQ) are the precursors of regression rank scores (RRS). The duality of RRS and RQ, both based on a common linear programming methodology, is an extension of tile duality of order statistics and vector of ranks.