# Finite-Sample Identification of Linear Regression Models with Residual-Permuted Sums

arXiv: https://arxiv.org/abs/2406.05440 · HTML: https://mlsanity.com/paper/2406.05440/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 8 Jun 2024.

## Builds on (most cited first, 4 of 4)

- [A Tutorial on the Non-Asymptotic Theory of System Identification](https://mlsanity.com/paper/2309.03873/) (2023)
- [Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models](https://mlsanity.com/paper/1807.08216/) (2018)
- [Perturbed Datasets Methods for Hypothesis Testing and Structure of Corresponding Confidence Sets](https://mlsanity.com/paper/1412.2352/) (2014)
- [Sign-Perturbed Sums (SPS) with Instrumental Variables for the Identification of ARX Systems - Extended Version](https://mlsanity.com/paper/1509.04774/) (2015)

## Built on by (most cited first, 1 of 1)

- [Finite Sample Analysis of Distribution-Free Confidence Ellipsoids for Linear Regression](https://mlsanity.com/paper/2409.08801/) (2024)

## Abstract (arXiv)

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.