Moindres carrés pondérés et poursuite

B. Bercu; M. Duflo

Annales de l'I.H.P. Probabilités et statistiques (1992)

  • Volume: 28, Issue: 3, page 403-430
  • ISSN: 0246-0203

How to cite

top

Bercu, B., and Duflo, M.. "Moindres carrés pondérés et poursuite." Annales de l'I.H.P. Probabilités et statistiques 28.3 (1992): 403-430. <http://eudml.org/doc/77440>.

@article{Bercu1992,
author = {Bercu, B., Duflo, M.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {weighted least-squares; linear time-invariant regression models; WLS parameter estimator; prediction errors; stochastic-gradient parameter estimator; weighted law of large numbers for vector-valued martingales; bounds on quadratic means; adaptive tracking problem; consistency; almost-surely guaranteed convergence rates},
language = {fre},
number = {3},
pages = {403-430},
publisher = {Gauthier-Villars},
title = {Moindres carrés pondérés et poursuite},
url = {http://eudml.org/doc/77440},
volume = {28},
year = {1992},
}

TY - JOUR
AU - Bercu, B.
AU - Duflo, M.
TI - Moindres carrés pondérés et poursuite
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1992
PB - Gauthier-Villars
VL - 28
IS - 3
SP - 403
EP - 430
LA - fre
KW - weighted least-squares; linear time-invariant regression models; WLS parameter estimator; prediction errors; stochastic-gradient parameter estimator; weighted law of large numbers for vector-valued martingales; bounds on quadratic means; adaptive tracking problem; consistency; almost-surely guaranteed convergence rates
UR - http://eudml.org/doc/77440
ER -

References

top
  1. [1] K.J. Aström et B. Wittenmark, On Self Tuning Regulators, Automatica, vol. 9, 1973, p.185-199. Zbl0249.93049
  2. [2] A.H. Becker, P.R. Kumar et C.Z. Wei, Adaptive Control with Stochastic Approximation Algorithm; Geometry of Convergence, I.E.E.E. trans. automatic control., vol. AC-30, 1985, p. 330-338. Zbl0591.93063MR786710
  3. [3] B. Bercu, Weighted Estimation and Tracking for ARMAX Models, Prépublication Université Paris-Sud, 1991. MR1153724
  4. [4] P. Caines, Stochastic Adaptive Control: Randomly Varying Parameters and Continually Disturbed Controls, Control science and technology for the progress of society, H. AKASHI éd., Pergamon, 1981, p. 925-930. MR736187
  5. [5] P. Caines, Linear Stochastic Systems, Wiley, 1988. Zbl0658.93003MR944080
  6. [6] P.E. Caines, S. Lafortune, Adaptive Control with Recursive Identification for Stochastic Linear Systems, I.E.E.E. Trans. Automatic Control, vol. AC-29, 1984, p. 312-321. Zbl0538.93071MR742364
  7. [7] H.F. Chen, Recursive System Identification and Adaptive Control by Use of the Modified Least Squares Algorithm, Siam J. Control Opt., vol. 22, 1984, p. 758-776. Zbl0554.93069MR755142
  8. [8] H.F. Chen et P.E. Caines, The Strong Consistency of the Stochastic Gradient Algorithm of Adaptive Control, I.E.E.E. Trans Automatic Control., vol. AC-30, 1985, p. 189-192. Zbl0555.93057MR778649
  9. [9] H.F. Chen et L. Guo, Convergence Rate for Least Squares Identification and Adaptive Control for Stochastic Systems, Int. J. Control., vol. 44, 1986, p. 1459-1476. Zbl0604.93061
  10. [10] H.F. Chen et L. Guo, Asymptotically Optimal Adaptive Control with Consistent Parameter Estimates, S.I.A.M. J. Control and Opt., vol. 25, 1987, p. 558-575. Zbl0619.93048MR885185
  11. [11] H.F. Chen et J.F. Zhang, Convergence Rates in Stochastic Adaptive Tracking, Int. J. Control, vol. 49, 1989, p.1915-1935. Zbl0683.93093MR1007689
  12. [12] M. Duflo, Méthodes récursives aléatoires, Masson, 1990. Zbl0703.62084MR1082344
  13. [13] M. Duflo, R. Senoussi et A. Touati, Sur la loi des grands nombres pour les martngales vectorielles et l'estimateur des moindres carrés d'un modèle de régression, Ann. Inst. Henri Poincaré, Ser. B., vol. 26, 1990, p. 549-566. Zbl0722.60031MR1080585
  14. [14] M. Duflo, R. Senoussi et A. Touati, Propriétés asymptotiques presque sûres de l'estimateur des moindres carrés d'un modèle autorégressif vectoriel, Ann. Inst. Henri Poincaré, Ser. B, vol. 27, 1991, p.1-25. Zbl0741.62083MR1098562
  15. [15] G.C. Goodwin, P.J. Ramdage et P.E. Caines, Discrete Time Stochastic Adaptive Control, SIAM J. Control Opt., vol. 19, 1981, p. 829-853. Zbl0473.93075MR634955
  16. [16] G.C. Goodwin et K.S. Sin, Adaptive Filtering, Prediction and Control, Prentice Hall, 1984. Zbl0653.93001
  17. [17] L. Guo et H.F. Chen, The Astrôm-Wittenmark Self Tuning Regulator Revisited and ELS-Based Adaptive Trackers, I.E.E.E. Trans. Automatic Control., vol. 36, 1991, p. 802-812. Zbl0752.93074MR1109818
  18. [18] H. Kaufmann, On the Strong Law of Large Numbers for Multivariate Martingales, Stochastic Processes Appl., vol. 26, 1987, p. 73-85. Zbl0632.60040MR917247
  19. [19] P.R. Kumar, Convergence of Adaptive Control Shemes Using Least Squares Parameter Estimates, I.E.E.E. Trans. Automatic Control., vol. 35, 1990, p.416-424. Zbl0716.93078MR1047993
  20. [20] P.R. Kumar et L. Praly, Self Tuning Trackers, S.I.A.M. J. control Opt., vol. 25, 1987, p.1053-1071. Zbl0627.93039MR893998
  21. [21] P.R. Kumar et P. Varaiya, Stochastic Systems: Estimation, Identification and Adaptive Control, Prentice Hall, 1986. Zbl0706.93057
  22. [22] T.L. Lai, Asymptotically Efficient Adaptive Control in Stochastic Regression Models, Adv. Appl. Math., vol. 7, 1986, p. 23-45. Zbl0615.93041MR834218
  23. [23] T.L. Lai et C.Z. Wei, Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems, Ann. Math. Stat., vol. 10, 1982, p. 154-166. Zbl0649.62060MR642726
  24. [24] T.L. Lai et C.Z. Wei, Asymptotic Properties of General Autoregressive Models and Strong Consistency of Least Squares Estimates and their Parameters, J. Multivariate Analysis, vol. 13, 1983, p.1-23. Zbl0509.62081MR695924
  25. [25] 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
  26. [26] T.L. Lai et C.Z. Wei, Extended Least Squares and their Applications to Adaptive Control and Prediction in Linear Systems, I.E.E.E. Trans. Automatic Control, vol. AC-31, 1986, p. 898-906. Zbl0603.93060MR855543
  27. [27] T.L. Lai et C.Z. Wei, Asymptotically Efficient Self Tuning Regulators, SIAM J. Control Optimization, vol. 25, 1987, p.466-481. Zbl0626.93034MR877072
  28. [28] A. Le Breton et M. Musiela, Consistency Sets of Least Squares Estimates in Stochastic Regression Models, dans « Stochastic Differential Systems », Lect. Notes Control Information Sci., n° 126, N. CHRISTOFEIT, K. HELMES, M. KOHLMAN éd., 1989. Zbl0679.62055MR1236070
  29. [29] K.S. Sin et G.C. Goodwin, Stochastic Adaptive Control Using a Modified Least Squares Algorithm, Automatica, J. I.F.A.C., vol. 18, 1982, p. 315-321. Zbl0489.93055MR665609
  30. [30] J.S. Wei, Adaptative Prediction of Least Squares Predictors in Stochastic Regression Models with Application to Time Series, Ann. Stat., vol. 15, 1987, p. 1667-1682. Zbl0643.62058MR913581

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.