J.C. Jarur and R.A. Rojas (Chile)
Correlation Functions, Confidence Regions, LSCR, Prediction Error.
We propose two refinements to the LSCR (Leave-Out Sign-Dominant Correlation Regions) method to improve the construction of confidence regions for parameters of identified models with a guaranteed probability. The LSCR method holds for any finite number of data points without using asymptotic theory, and previous knowledge on the noise affecting the data is reduced to a minimum. We prove the exact probability for the general confidence region instead of just a probability bound as it is the current situation. We also detect an accuracy problem when using a straightforward implementation of the LSCR algorithm and provide a solution by taking advantage of the new found exact probability expression. The theory is validated with empirical results based on Monte Carlo simulations on open loop and closed loop systems.
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