Finite Sample Confidence Region for EIV Systems Using Regression Model
Errors-In-Variables (EIV) models in which both input and output data are contaminated by noise have applications in signal processing. We propose a method for constructing non-asymptotic confidence regions for the parameters of EIV models. The method is based on the Leave-out Sign-dominant Correlation Regions (LSCR) principle which gives probabilistically guaranteed confidence region when the input is measured without noise. A regression model is utilized to extend LSCR to EIV systems. The newly established regression vector contains the past outputs and the estimated past inputs. It is shown that the corresponding prediction error has the desired properties such that it can be used to form correlation functions from which confidence regions can be constructed. For any finite number of data points it is proved that the region contains the true parameter with a user-chosen probability.
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