# Perturbed Datasets Methods for Hypothesis Testing and Structure of Corresponding Confidence Sets

arXiv: https://arxiv.org/abs/1412.2352 · HTML: https://mlsanity.com/paper/1412.2352/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2014.

## Built on by (most cited first, 5 of 5)

- [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)
- [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)
- [Robust Independence Tests with Finite Sample Guarantees for Synchronous Stochastic Linear Systems](https://mlsanity.com/paper/2308.02054/) (2023)

## Abstract (arXiv)

Hypothesis testing methods that do not rely on exact distribution assumptions have been emerging lately. The method of sign-perturbed sums (SPS) is capable of characterizing confidence regions with exact confidence levels for linear regression and linear dynamical systems parameter estimation problems if the noise distribution is symmetric. This paper describes a general family of hypothesis testing methods that have an exact user chosen confidence level based on finite sample count and without relying on an assumed noise distribution. It is shown that the SPS method belongs to this family and we provide another hypothesis test for the case where the symmetry assumption is replaced with exchangeability. In the case of linear regression problems it is shown that the confidence regions are connected, bounded and possibly non-convex sets in both cases. To highlight the importance of understanding the structure of confidence regions corresponding to such hypothesis tests it is shown that confidence sets for linear dynamical systems parameter estimates generated using the SPS method can have non-connected parts, which have far reaching consequences.