Distribution theory of rank statistics: Distribution Theory of Linear Rank-Order Statistics Distribution Theory of Signed Rank Order Statistics Distribution Theory of Multivariate Linear Rank-Order Statistics Nonparametric inference in linear models: Distribution-Free Rank-Order Tests for Some Linear Hypotheses Rank-Order Estimation Theory in Some Linear Models Asymptotically Distribution-Free Aligned Rank- Order Tests for Some General Linear Hypotheses Rank-Order Tests for Miscellaneous Problems in Linear Models Appendix.
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Atkinson et al. (1986) studied this question.