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1.
  • Agüero, Juan C., et al. (författare)
  • Accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation
  • 2012
  • Ingår i: Automatica. - 0005-1098. ; 48:4, s. 632-637
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we study the accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation. We present a frequency-domain representation for the information matrix for general linear MIMO models. We show that the variance of estimated parametric models for linear MIMO systems satisfies a fundamental integral trade-off. This trade-off is expressed as a multivariable 'water-bed' effect. An extension to spectral estimation is also discussed.
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2.
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3.
  • Akçay, Hüseyin, et al. (författare)
  • On the Choice of Norms in System Identification
  • 1994
  • Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - 9780080422251 ; s. 103-108
  • Konferensbidrag (refereegranskat)abstract
    • In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).
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4.
  • Akçay, Hüseyin, et al. (författare)
  • On the Choice of Norms in System Identification
  • 1994
  • Rapport (övrigt vetenskapligt)abstract
    • In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).
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5.
  • Akcay, H., et al. (författare)
  • On the choice of norms in system identification
  • 1996
  • Ingår i: IEEE Transactions on Automatic Control. - 00189286 (ISSN). ; 41:9, s. 1367-1372
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all â„“p-norms, p ≀ 2 < ∞ for F(C). ©1996 IEEE.
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6.
  • Akçay, Hüseyin, et al. (författare)
  • On the Choice of Norms in System Identification
  • 1995
  • Rapport (övrigt vetenskapligt)abstract
    • In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).
  •  
7.
  • Akçay, Hüseyin, et al. (författare)
  • On the Choice of Norms in System Identification
  • 1996
  • Rapport (övrigt vetenskapligt)abstract
    • In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).
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8.
  • Akçay, Hüseyin, et al. (författare)
  • The Least-Squares Identification of FIR Systems Subject to Worst-Case Noise
  • 1993
  • Rapport (övrigt vetenskapligt)abstract
    • The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the lest-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.
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9.
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10.
  • Akçay, Hüseyin, et al. (författare)
  • The Least-Squares Identification of FIR Systems Subject to Worst-Case Noise
  • 1994
  • Rapport (övrigt vetenskapligt)abstract
    • The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the least-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.
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