Rank Tests of Sub-Hypotheses in the General Linear Regression

Abstract

This paper considers the general linear regression model $Y_i = \sum_j \beta_j x_{ij} + \varepsilon_i$, and studies the problem of testing hypotheses about some of the $\beta$'s while regarding others as nuisance parameters. The test criteria discussed, which are based on ranks of residuals, are shown to be asymptotically distribution-free.