Parameter identification for nonlinear systems: Guaranteed confidence regions through LSCR

Università degli Studi di Brescia, Brescia, Lombardy, Italy
Automatica (Impact Factor: 3.02). 08/2007; 43(8):1418-1425. DOI: 10.1016/j.automatica.2007.01.016
Source: DBLP


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∼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. 2007 Elsevier Ltd. All rights reserved.

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    • "There is a growing interest for developing methods that do not rely on the central limit theorem or on Gaussian assumptions about the noise ([3], [4], [5], [6], [7]). The 16 th IFAC Symposium on System Identification had a plenary session dedicated to this topic [2]. "
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    ABSTRACT: Hypothesis testing methods that do not rely on exact distribution assumptions have been emerging lately. The method of sign-perturbed sums (SPS) is capable of characterizing confidence regions with exact confidence levels for linear regression and linear dynamical systems parameter estimation problems if the noise distribution is symmetric. This paper describes a general family of hypothesis testing methods that have an exact user chosen confidence level based on finite sample count and without relying on an assumed noise distribution. It is shown that the SPS method belongs to this family and we provide another hypothesis test for the case where the symmetry assumption is replaced with exchangeability. In the case of linear regression problems it is shown that the confidence regions are connected, bounded and possibly non-convex sets in both cases. To highlight the importance of understanding the structure of confidence regions corresponding to such hypothesis tests it is shown that confidence sets for linear dynamical systems parameter estimates generated using the SPS method can have non-connected parts, which have far reaching consequences.
    Automatica 11/2014; 51. DOI:10.1016/j.automatica.2014.10.083 · 3.02 Impact Factor
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    • "Cette hypothèse donne un sensà la notion de vraie valeur pour le vecteur des paramètres. Dans [1] [2] [3], deux nouvelles approches nommées LSCR et SPS sont introduites pour obtenir une caractérisation exacte de 1. Ce travail a ´ eté en partie financé par l'ANR CPP. l'incertitude paramétrique dans des conditions non-asymptotiques . "

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    ABSTRACT: We propose a new finite sample system identification method, called Sign-Perturbed Sums (SPS), to estimate the parameters of dynamical systems under mild statistical assump-tions. The proposed method constructs non-asymptotic confidence regions that include the least-squares (LS) estimate and are guaranteed to contain the true parameters with a user-chosen exact probability. Our method builds on ideas imported from the "Leave-out Sign-dominant Correlation Regions" (LSCR) approach, but, unlike LSCR, also guarantees the inclusion of the LS estimate and provides confidence regions for multiple parameters with exact probabilities. This paper presents the SPS method for FIR and ARX systems together with its main theoretical properties, as well as demonstrates the approach through simple examples and experiments.
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