A novel algorithm for confidence sub-contour box estimation: an alternative to traditional confidence intervals

TL;DR

This paper introduces a new algorithm for estimating confidence sub-contour boxes (CSB) in non-linear models, providing a computationally efficient alternative to traditional confidence intervals with enhanced interpretability.

Contribution

The paper proposes two novel algorithms for CSB estimation, offering a new approach to confidence region estimation that addresses issues with existing methods as the number of factors increases.

Findings

Validated properties of CSB including uncertainty level and asymmetry

Demonstrated sensitivity assessment capability for each factor

Identified true-influential factors effectively

Abstract

The factor estimation process is a really challenging task for non-linear models. Even whether researchers manage to successfully estimate model factors, they still must estimate their confidence intervals, which could require a high computational cost to turn them into informative measures. Some methods in the literature attempt to estimate regions within the estimation search space where factors may jointly exist and fit the real data (confidence contours), however, its estimation process raises several issues as the number of factors increases. Hence, in this paper, we focus on the estimation of a subregion within the confidence contour that we called as Confidence Subcontour Box (CSB). We proposed two main algorithms for CSB estimation, as well as its interpretation and validation. Given the way we estimated CSB, we expected and validated some useful properties of this new kind of confidence interval: a user-defined uncertainty level, asymmetrical intervals, sensitivity assessment related to the interval length for each factor, and the identification of true-influential factors.