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This paper presents a novel sample-based method for constructing confidence polytopes in linear regression models with endogenous regressor. Our approach uses independent noise sequence samples and an ordering property to form confidence regions that contain the true system parameter with a user-specified lower bounded probability, regardless of sample size. By intersecting multiple regions derived from this ordering, we obtain a conservative estimate that guarantees a lower probability bound. The desired probability bound can be flexibly adjusted by selecting appropriate rational numbers. Moreover, a scenario-based method called the wait-and-judge technique is used to evaluate the probability that the true system parameter is included within the sampled convex hull. Numerical simulation is provided to help illustrate the theorem.

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Sample-Based Confidence Polytope for Linear Regression Model with Endogenous Regressors: Guaranteed Probabilistic Lower Bounds

  • 会议论文

  • 发表日期：

    2026年

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  • Xiaopuwen Wang,
  • Jintao Ding,
  • Ping Yue,
  • Li Zheng

摘要

This paper presents a novel sample-based method for constructing confidence polytopes in linear regression models with endogenous regressor. Our approach uses independent noise sequence samples and an ordering property to form confidence regions that contain the true system parameter with a user-specified lower bounded probability, regardless of sample size. By intersecting multiple regions derived from this ordering, we obtain a conservative estimate that guarantees a lower probability bound. The desired probability bound can be flexibly adjusted by selecting appropriate rational numbers. Moreover, a scenario-based method called the wait-and-judge technique is used to evaluate the probability that the true system parameter is included within the sampled convex hull. Numerical simulation is provided to help illustrate the theorem.