Abstract

In this paper we consider the problem of constructing confidence regions for the parameters of nonlinear dynamical systems. The proposed method uses higher order statistics and extends the LSCR (leave-out sign-dominant correlation regions) algorithm for linear systems introduced in Campi and Weyer [2005, Guaranteed non-asymptotic confidence regions in system identification. Automatica 41(10), 1751–1764. Extended version available at http://www.ing.unibs.it/campi]. The confidence regions contain the true parameter value with a guaranteed probability for any finite number of data points. Moreover, the confidence regions shrink around the true parameter value as the number of data points increases. The usefulness of the proposed approach is illustrated on some simple examples.

Keywords: Confidence sets; Finite sample results; Nonlinear system identification

Article Outline

1. Introduction

2. A simple nonlinear example: from second to higher order statistics

3. Extension of LSCR to higher order statistics

3.1. Construction of the confidence region

3.2. Asymptotic behavior

4. Application example: a simple bilinear system

5. Conclusion

Acknowledgements

Appendix A. Proofs

A.1. Proof of Theorem 1

A.2. Proof of Theorem 4

A.3. Group construction

References

Vitae