Authors:
Ajay Jaswanth, Yuvan Adith, M. Mohan, R. Vinoth

Addresses:
Department of Artificial Intelligence and Machine Learning, SRM Institute of Science and Technology, Ramapuram, Chennai, Tamil Nadu, India. Department of Computer Science and Engineering in AIML, SRM Institute of Science and Technology, Ramapuram, Chennai, Tamil Nadu, India.

Abstract:

This paper addresses the basic problem of constructing confidence regions with statistical properties for the parameters of a linear regression model, without imposing strong distributional assumptions on the errors. Classical methods all make the same assumptions: Normally distributed residuals with constant variance, which are not always satisfied in empirical applications, especially when sample sizes are small or when normality and heteroscedasticity are violated. To alleviate these restrictive conditions, researchers propose a principled distribution-free methodology for constructing confidence ellipsoids that provides valid inferential guarantees with minimal assumptions. The method employs resampling techniques, such as the residual bootstrap and the pairs bootstrap, along with an empirical estimate of the covariance structure that requires no parametric assumptions. This allows the method to characterize the sampling distribution of the LS estimator. Extensive simulation experiments have shown that these ellipsoidal regions achieve almost optimal coverage probabilities. Using real-world examples from economics, biomedicine, and the environment, the method's applicability and use are further demonstrated. 

Keywords: Distribution-Free Inference; Confidence Ellipsoids; Linear Regression; Finite Sample Analysis; Robust Statistics; Parametric Estimation; Coverage Probability; Bootstrap Methods.

Received on: 16/09/2024, Revised on: 09/12/2024, Accepted on: 18/04/2025, Published on: 07/05/2026

DOI: 10.69888/FTSASS.2026.000649

FMDB Transactions on Sustainable Applied Sciences, 2026 Vol. 3 No. 1, Pages: 47–61

• Views : 35
• Downloads : 11

Download PDF