Sur l'estimateur des moindres carrés généralisé d'un modèle ARMAX. Application à l'identification des modèles ARMA

B. Bercu

Annales de l'I.H.P. Probabilités et statistiques (1991)

  • Volume: 27, Issue: 3, page 425-443
  • ISSN: 0246-0203

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Bercu, B.. "Sur l'estimateur des moindres carrés généralisé d'un modèle ARMAX. Application à l'identification des modèles ARMA." Annales de l'I.H.P. Probabilités et statistiques 27.3 (1991): 425-443. <http://eudml.org/doc/77412>.

@article{Bercu1991,
author = {Bercu, B.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stable cases; complex multivariate ARMAX model; strong consistency; extended least squares estimator; recursive AML scheme; hypothesis of passivity; almost sure rates of convergence; prediction errors; almost sure asymptotic behaviour of trajectories; complex multivariate ARMA model; unstable cases; explosive regular case},
language = {fre},
number = {3},
pages = {425-443},
publisher = {Gauthier-Villars},
title = {Sur l'estimateur des moindres carrés généralisé d'un modèle ARMAX. Application à l'identification des modèles ARMA},
url = {http://eudml.org/doc/77412},
volume = {27},
year = {1991},
}

TY - JOUR
AU - Bercu, B.
TI - Sur l'estimateur des moindres carrés généralisé d'un modèle ARMAX. Application à l'identification des modèles ARMA
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1991
PB - Gauthier-Villars
VL - 27
IS - 3
SP - 425
EP - 443
LA - fre
KW - stable cases; complex multivariate ARMAX model; strong consistency; extended least squares estimator; recursive AML scheme; hypothesis of passivity; almost sure rates of convergence; prediction errors; almost sure asymptotic behaviour of trajectories; complex multivariate ARMA model; unstable cases; explosive regular case
UR - http://eudml.org/doc/77412
ER -

References

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  1. [1] P.E. Caines, Linear Stochastic Systems, Wiley, 1988. Zbl0658.93003MR944080
  2. [2] Y.S. Chow, Local Convergence of Martingales and the Law of Large Numbers, Ann. Math. Stat., vol. 36, 1965, p. 493-507. Zbl0134.34003MR182040
  3. [3] M. Duflo, Méthodes Récursives Aléatoires, Masson, 1990. Zbl0703.62084MR1082344
  4. [4] M. Duflo, R. Senoussi et A. Touati, Propriétés asymptotiques presque sûres de l'estimateur des moindres carrés d'un modèle autorégressif vectoriel, Ann. Inst. H. Poincaré, vol. 27, 1991, p. 1-25. Zbl0741.62083MR1098562
  5. [5] G.C. Goodwin, P.J. Ramadge et P.E. Caines, Discrete Time Stochastic Adaptive Control, S.I.A.M. J. Control and Optimization, vol. 19, 1981, p. 829-853. Zbl0473.93075MR634955
  6. [6] T.L. Lai et C.Z. Wei, Least SquaresEstimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems, Ann. Statistics, vol. 10, 1982, p. 154-166. Zbl0649.62060MR642726
  7. [7] T.L. Lai et C.Z. Wei, Asymptotic Properties of General Autoregressive Models and Strong Consistency of Least Squares Estimates of Their Parameters, J. Mult. Anal., vol. 13, 1983, p. 1-23. Zbl0509.62081MR695924
  8. [8] T.L. Lai et C.Z. Wei, Extended LeastSquares and Their Applications to Adaptive Control and Prediction in Linear Systems, I.E.E.E. trans. automatic control., vol. AC-31, n° 10, 1986, p. 898-906. Zbl0603.93060MR855543
  9. [9] T.L. Lai et C.Z. Wei, On the Concept of Excitation in Least Squares Identification and Adaptive Control, Stochastics, vol. 16, 1986, p. 227-254. Zbl0595.60048MR837613
  10. [10] T.L. Lai et C.Z. Wei, Asymptotically Efficient Self-Tuning Regulators, S.I.A.M. J. Control Opt., vol. 25, n° 2, 1987, p. 466-481. Zbl0626.93034MR877072
  11. [11] C.R. Rao, Linear Statistical Inference and Its Appl., Wiley, 1965. Zbl0137.36203MR221616
  12. [12] V. Solo, The Convergence of AML, I.E.E.E. Trans. Automatic Control., vol. AC-24, n° 6, 1979, p. 958-962. Zbl0422.62083

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