Randomization empirical processes
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This article serves as a link between two well-established fields in mathematical statistics: empirical processes and inference based on randomization via algebraic groups. To this end, a broadly applicable conditional Donsker theorem is developed for empirical processes which are based on randomized observations. Random elements of an algebraic group are applied to the data vectors from which the randomized version of a statistic is derived. Combining a variant of the functional delta-method with a suitable studentization of the statistic, asymptotically exact hypothesis tests can be deduced, while the finite sample exactness property under group-invariant sub-hypotheses is preserved. The methodology is exemplified with two examples: Pearson's correlation coefficient and a Mann-Whitney-type effect based on right-censored paired data.
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