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.

翻译：本文研究一种无分布、有限样本的数据扰动方法——残差置换和算法，作为符号扰动和算法的替代方案，用于构建置信域。符号扰动和算法要求噪声项独立（但可随时间变化）且关于零对称，而残差置换和算法则放宽了对称性假设，仅要求噪声独立同分布。其核心思想在于对残差进行置换操作而非扰动其符号。本文以灵活的方式引入残差置换和算法，允许多种设计选择。该方法具有精确的有限样本覆盖概率，我们首次证明了在一般性假设下，此类基于置换的置信域具有一致强相合性，即当样本量增加时，残差置换和置信域几乎必然收缩至真实参数值附近。同时，我们将符号扰动和算法的椭球外逼近方法推广至残差置换和算法，并通过数值实验验证了该方法的有效性。