Abstract
Abstract Permutation tests of hypotheses about parameters in linear models derive their validity from exchangeability of the errors in the null model. These errors are unobservable but differ from the observable residuals by a constant for any hypothesis that posits a null, reduced parameter model with just an intercept term. For these hypotheses, exact permutation inferences are possible for iid error distributions of any form. Other hypotheses on subsets of parameters in multiple regression models are not exact because the residuals are not exchangeable with equal probability. Several options to improve exchangeability for these hypotheses have been developed and are presented for permutation tests on quantile regression estimates of the linear model.
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