  This letter studies a distribution-free, finite-sample data perturbation (DP)
method, the Residual-Permuted Sums (RPS), which is an alternative of the
Sign-Perturbed Sums (SPS) algorithm, to construct confidence regions. While SPS
assumes independent (but potentially time-varying) noise terms which are
symmetric about zero, RPS gets rid of the symmetricity assumption, but assumes
i.i.d. noises. The main idea is that RPS permutes the residuals instead of
perturbing their signs. This letter introduces RPS in a flexible way, which
allows various design-choices. RPS has exact finite sample coverage
probabilities and we provide the first proof that these permutation-based
confidence regions are uniformly strongly consistent under general assumptions.
This means that the RPS regions almost surely shrink around the true parameters
as the sample size increases. The ellipsoidal outer-approximation (EOA) of SPS
is also extended to RPS, and the effectiveness of RPS is validated by numerical
experiments, as well.
