Confidence Polytope with Guaranteed Probabilistic Lower Bounds in Linear Regression Model With Deterministic Regressor

This paper introduces a new method for constructing guaranteed probabilistic lower bounded confidence polytope in linear regression model with deterministic regressor. The proposed algorithm generates non-asymptotic confidence regions around the least-squares estimate, ensuring that the true parameter lies within the polytope with a lower bounded probability predetermined by the user. By drawing independent samples from the noise distribution and leveraging specific ordering properties of independent and identically distributed random variables, the method efficiently builds these confidence polytopes. A key assumption of the approach is the availability of a known joint density function for the noise, enabling accurate sampling. The performance and reliability of the method are demonstrated through a simulation of an FIR system, with comparisons to confidence regions obtained from other non-asymptotic system identification methods.