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We propose a class of tests for linear regression on concomitants (inducedorder statistics). These tests are based on sequential sums of regressionresiduals. We self-center and self-normalize these sums. The resulting processis called an empirical bridge. We prove weak convergence of the empiricalbridge in uniform metrics to a centered Gaussian process. The proposed testsare of chi-square type.

Asymptotics of an empirical bridge of regression on induced order statistics