# Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models

arXiv: https://arxiv.org/abs/1807.08216 · HTML: https://mlsanity.com/paper/1807.08216/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2018.

## Built on by (most cited first, 14 of 14)

- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Nonparametric, Nonasymptotic Confidence Bands with Paley-Wiener Kernels for Band-Limited Functions](https://mlsanity.com/paper/2206.13629/) (2022)
- [Improving Kernel-Based Nonasymptotic Simultaneous Confidence Bands](https://mlsanity.com/paper/2401.15791/) (2024)
- [Sample Complexity of the Sign-Perturbed Sums Identification Method: Scalar Case](https://mlsanity.com/paper/2401.15792/) (2024)
- [Data-Driven Upper Confidence Bounds with Near-Optimal Regret for Heavy-Tailed Bandits](https://mlsanity.com/paper/2406.05710/) (2024)
- [From Conformal Predictions to Confidence Regions](https://mlsanity.com/paper/2405.18601/) (2024)
- [Finite Sample Confidence Regions for Linear Regression Parameters Using Arbitrary Predictors](https://mlsanity.com/paper/2401.15254/) (2024)
- [Finite-Sample Identification of Linear Regression Models with Residual-Permuted Sums](https://mlsanity.com/paper/2406.05440/) (2024)
- [Sample Complexity of the Sign-Perturbed Sums Method](https://mlsanity.com/paper/2409.01243/) (2024)
- [Resampled Confidence Regions with Exponential Shrinkage for the Regression Function of Binary Classification](https://mlsanity.com/paper/2308.01835/) (2023)
- [Robust Independence Tests with Finite Sample Guarantees for Synchronous Stochastic Linear Systems](https://mlsanity.com/paper/2308.02054/) (2023)
- [Finite Sample Analysis of Distribution-Free Confidence Ellipsoids for Linear Regression](https://mlsanity.com/paper/2409.08801/) (2024)
- [Mesters'eges Intelligencia Kutat'asok Magyarorsz'agon](https://mlsanity.com/paper/2503.05767/) (2025)
- [MiNCE: Nonparametric, Strongly Consistent Confidence Envelopes for Band-Limited Functions and their Smoothed Spectra](https://mlsanity.com/paper/2609.09436/) (2026)

## Abstract (arXiv)

We propose a new system identification method, called Sign-Perturbed Sums (SPS), for constructing non-asymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not limited to FIR systems, and we show that the SPS confidence regions have exact confidence probabilities, i.e., they contain the true parameter with a user-chosen exact probability for any finite data set. Moreover, we also prove that the SPS regions are star convex with the Least-Squares (LS) estimate as a star center. The main assumptions of SPS are that the noise terms are independent and symmetrically distributed about zero, but they can be nonstationary, and their distributions need not be known. The paper also proposes a computationally efficient ellipsoidal outer approximation algorithm for SPS. Finally, SPS is demonstrated through a number of simulation experiments.