Finite Sample Confidence Regions for Linear Regression Parameters Using Arbitrary Predictors

• URL: http://arxiv.org/abs/2401.15254v1
• Date: Sat, 27 Jan 2024 00:15:48 GMT
• Title: Finite Sample Confidence Regions for Linear Regression Parameters Using Arbitrary Predictors
• Authors: Charles Guille-Escuret and Eugene Ndiaye
• Abstract summary: We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. The derived confidence regions can be cast as constraints within a Mixed Linear Programming framework, enabling optimisation of linear objectives. Unlike previous methods, the confidence region can be empty, which can be used for hypothesis testing.
• Score: 1.6860963320038902
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions deviating from strict linearity up to some adjustable threshold, thereby accommodating a comprehensive and pragmatically relevant set of functions. The derived confidence regions can be cast as constraints within a Mixed Integer Linear Programming framework, enabling optimisation of linear objectives. This representation enables robust optimization and the extraction of confidence intervals for specific parameter coordinates. Unlike previous methods, the confidence region can be empty, which can be used for hypothesis testing. Finally, we validate the empirical applicability of our method on synthetic data.

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