Article

Parameter identification for nonlinear systems: Guaranteed confidence regions through LSCR.

Automatica (Impact Factor: 2.92). 01/2007; 43:1418-1425. DOI: 10.1016/j.automatica.2007.01.016
Source: DBLP

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 athttp://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. 2007 Elsevier Ltd. All rights reserved.

0 Bookmarks
 · 
55 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, the problem of estimating uncertainty regions for identiÿed models is considered. A typical approach in this context is to resort to the asymptotic theory of Prediction Error Methods for system identiÿcation, by means of which ellipsoidal uncertainty regions can be constructed for the uncertain parameters. We show that the uncertainty regions worked out through the asymptotic theory can be unreliable in certain situations, precisely characterized in the paper. Then, we critically analyze the theoretical conditions for the validity of the asymptotic theory, and prove that the asymptotic theory also applies under new assumptions which are less restrictive than the usually required ones. Thanks to this result, we single out the classes of models among standard ones (ARX, ARMAX, Box–Jenkins, etc.) where the asymptotic theory can be safely used in practical applications to assess the quality of the identiÿed model. These results are of interest in many applications, including iterative controller design schemes.
    Automatica. 01/2004; 40:1319-1332.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The linearity of a time series is tested by use of the bispectrum. We define the time series to be linear if the best predictor is linear. The bispectrum is estimated by stretching the data and smoothing by the Subba Rao–Gabr optimal window. The null hypothesis tested here is that the best predictor is linear against the alternative that the best predictor is quadratic. It turns out that the test statistic is asymptotically χ2-distributed under the hypothesis that the time series is linear. The results are demonstrated using simulated and real data.
    Journal of Time Series Analysis 10/1998; 19(6):737 - 753. · 0.79 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Subsamples are used to generate confidence intervals for a parameter of a linear regression model, under the assumption that the error variables are independent, continuous and symmetric about 0 in distribution.
    The Annals of Mathematical Statistics 01/1970;

Full-text

View
0 Downloads
Available from