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Volumn 16, Issue 3, 2006, Pages 741-772

Efficient recursive estimation and adaptive control in stochastic regression and armax models

Author keywords

Adaptive control; Asymptotic efficiency; Least squares; M estimators; Semiparametric estimation; Stochastic regression; Strong consistency

Indexed keywords


EID: 33750972856     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (3)

References (58)
  • 1
    • 0006231196 scopus 로고
    • Some experimental results on the statistical problem of least squares estimates in control problems
    • Anderson, T. W. and Taylor, J. (1976). Some experimental results on the statistical problem of least squares estimates in control problems. Econometrica 44, 1289-1302.
    • (1976) Econometrica , vol.44 , pp. 1289-1302
    • Anderson, T.W.1    Taylor, J.2
  • 2
    • 27844497379 scopus 로고
    • On some price adjustment schemes
    • Aokoi, M. (1974). On some price adjustment schemes. Ann. Econ. Soc. Measurements 3, 95-116.
    • (1974) Ann. Econ. Soc. Measurements , vol.3 , pp. 95-116
    • Aokoi, M.1
  • 3
    • 0015035795 scopus 로고
    • System identification - A survey
    • Åström, K. and Eykhof, P. (1971). System identification - a survey. Automatica 7, 123-167.
    • (1971) Automatica , vol.7 , pp. 123-167
    • Åström, K.1    Eykhof, P.2
  • 4
    • 0001642818 scopus 로고
    • On self-tuning regulators
    • Åström, K. and Wittenmark, B. (1973). On self-tuning regulators. Automatica 9, 195-199.
    • (1973) Automatica , vol.9 , pp. 195-199
    • Åström, K.1    Wittenmark, B.2
  • 5
    • 0010678717 scopus 로고
    • Über einige Eigenschaften der lacunaren trigonometrishe Reihen
    • Banach, S. (1930). Über einige Eigenschaften der lacunaren trigonometrishe Reihen. Studio, Math. 2, 207-220.
    • (1930) Studio, Math. , vol.2 , pp. 207-220
    • Banach, S.1
  • 6
    • 0000947808 scopus 로고
    • On adaptive estimation
    • Bickel, P. J. (1982). On adaptive estimation. Ann. Statist. 10, 647-671.
    • (1982) Ann. Statist. , vol.10 , pp. 647-671
    • Bickel, P.J.1
  • 7
    • 0022044787 scopus 로고
    • Adaptive control with stochastic approximation algorithm: Geometry and convergence
    • Becker, A., Kumar, P. R. and Wei, C. Z. (1985). Adaptive control with stochastic approximation algorithm: geometry and convergence. IEEE Trans. Automat. Control 30, 330-338.
    • (1985) IEEE Trans. Automat. Control , vol.30 , pp. 330-338
    • Becker, A.1    Kumar, P.R.2    Wei, C.Z.3
  • 8
    • 0021406121 scopus 로고
    • Adaptive control with recursive identification for stochastic linear systems
    • Caines, P. E. and Lafortune, S. (1984). Adaptive control with recursive identification for stochastic linear systems. IEEE Trans. Automat. Control AC-29, 312-321.
    • (1984) IEEE Trans. Automat. Control , vol.AC-29 , pp. 312-321
    • Caines, P.E.1    Lafortune, S.2
  • 9
    • 33751018248 scopus 로고    scopus 로고
    • Inference in time series and stochastic processes
    • Chan, N. H. (2006). Inference in time series and stochastic processes. Statist. Sinica 16, 683-696.
    • (2006) Statist. Sinica , vol.16 , pp. 683-696
    • Chan, N.H.1
  • 10
    • 0001110724 scopus 로고
    • Convergence systems and strong consistency of least squares estimates in regression model
    • Chen, G. J., Lai, T. L. and Wei, C. Z. (1981). Convergence systems and strong consistency of least squares estimates in regression model. J. Multivariate Anal. 11, 319-333.
    • (1981) J. Multivariate Anal. , vol.11 , pp. 319-333
    • Chen, G.J.1    Lai, T.L.2    Wei, C.Z.3
  • 11
    • 0011428483 scopus 로고
    • On estimation and adaptive estimation for locally asymptotically normal families
    • Fabian, V. and Hannan, J. (1982). On estimation and adaptive estimation for locally asymptotically normal families. Z. Wahrsch. Verw. Gebiete 59, 459-478.
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.59 , pp. 459-478
    • Fabian, V.1    Hannan, J.2
  • 12
    • 0011716051 scopus 로고
    • The theory of dual control I-II
    • 1022-1039
    • Feldbaum, A. A. (1961). The theory of dual control I-II. Autom. Remote Control 21, 874-883, 1022-1039.
    • (1961) Autom. Remote Control , vol.21 , pp. 874-883
    • Feldbaum, A.A.1
  • 13
    • 0001778866 scopus 로고
    • Lacunary series and independent functions
    • Gaposhkin, V. F. (1966). Lacunary series and independent functions. Russian Math. Surveys 216, 1-82.
    • (1966) Russian Math. Surveys , vol.216 , pp. 1-82
    • Gaposhkin, V.F.1
  • 14
    • 0007298844 scopus 로고
    • On stochastic approximation
    • Gladyshev, E. G. (1965). On stochastic approximation. Theory Probab. Appl. 10, 275-278.
    • (1965) Theory Probab. Appl. , vol.10 , pp. 275-278
    • Gladyshev, E.G.1
  • 16
    • 0029270662 scopus 로고
    • Convergence and logarithmic laws of self-tuning regulators
    • Guo, L. (1995). Convergence and logarithmic laws of self-tuning regulators. Automatica 31, 435-450.
    • (1995) Automatica , vol.31 , pp. 435-450
    • Guo, L.1
  • 17
    • 33750982029 scopus 로고
    • Convergence rate of ELS based adaptive tracker
    • Guo, L. and Chen, H. F. (1988). Convergence rate of ELS based adaptive tracker. Syst. Sci & Math. Sci. 1, 131-138.
    • (1988) Syst. Sci & Math. Sci. , vol.1 , pp. 131-138
    • Guo, L.1    Chen, H.F.2
  • 18
    • 0026188682 scopus 로고
    • The Åström-Wittenmark self-tuning regulator revisited and ELS-baaed adaptive trackers
    • Guo, L. and Chen, H. F. (1991). The Åström-Wittenmark self-tuning regulator revisited and ELS-baaed adaptive trackers. IEEE Trans. Automat. Control 36, 802-812.
    • (1991) IEEE Trans. Automat. Control , vol.36 , pp. 802-812
    • Guo, L.1    Chen, H.F.2
  • 19
    • 33750980309 scopus 로고    scopus 로고
    • Approximate policy optimization and adaptive control in regression models
    • To appear
    • Han, J., Lai, T. L. and Spivakovsky, V. (2005). Approximate policy optimization and adaptive control in regression models. To appear in Computational Economics.
    • (2005) Computational Economics
    • Han, J.1    Lai, T.L.2    Spivakovsky, V.3
  • 20
    • 0000414660 scopus 로고
    • Large sample properties of generalized method of moments estimators
    • Hansen, L. (1982). Large sample properties of generalized method of moments estimators. Econometrica 50, 1029-1054.
    • (1982) Econometrica , vol.50 , pp. 1029-1054
    • Hansen, L.1
  • 21
    • 0000262302 scopus 로고
    • On adaptive estimation in stationary ARMA processes
    • Kreiss, J-P. (1987). On adaptive estimation in stationary ARMA processes. Ann. Statist. 15, 112-133.
    • (1987) Ann. Statist. , vol.15 , pp. 112-133
    • Kreiss, J.-P.1
  • 22
    • 38249041669 scopus 로고
    • Asymptotically efficient adaptive control in stochastic regression models
    • Lai, T. L. (1986). Asymptotically efficient adaptive control in stochastic regression models. Adv. Appl. Math. 7, 23-45.
    • (1986) Adv. Appl. Math. , vol.7 , pp. 23-45
    • Lai, T.L.1
  • 23
    • 0038026196 scopus 로고    scopus 로고
    • Stochastic approximation
    • Lai, T. L. (2003). Stochastic approximation. Ann. Statist. 31, 391-406.
    • (2003) Ann. Statist. , vol.31 , pp. 391-406
    • Lai, T.L.1
  • 24
    • 18744437942 scopus 로고
    • Strong consistency of least-squares estimates in regression models
    • Lai, T.L. and Robbins, H. (1977). Strong consistency of least-squares estimates in regression models. Proc. Natl. Acad. Sci. USA 74, 2667-2669.
    • (1977) Proc. Natl. Acad. Sci. USA , vol.74 , pp. 2667-2669
    • Lai, T.L.1    Robbins, H.2
  • 25
    • 0000878355 scopus 로고
    • Adaptive design and stochastic approximation
    • Lai, T. L. and Robbins, H. (1979). Adaptive design and stochastic approximation. Ann. Statis. 7, 1196-1221.
    • (1979) Ann. Statis. , vol.7 , pp. 1196-1221
    • Lai, T.L.1    Robbins, H.2
  • 26
    • 0000797191 scopus 로고
    • Consistency and asymptotic efficiency of slope in stochastic: Approximation schemes
    • Lai, T. L. and Robbins, H. (1981). Consistency and asymptotic efficiency of slope in stochastic: approximation schemes. Z. Wahrsch. Verw. Gebiete 56, 329-360.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.56 , pp. 329-360
    • Lai, T.L.1    Robbins, H.2
  • 27
    • 0011531259 scopus 로고
    • Iterated least squares in multiperiod control
    • Lai, T.L. and Robbins, H. (1982). Iterated least squares in multiperiod control. Adv. Appl. Math. 3, 50-73.
    • (1982) Adv. Appl. Math. , vol.3 , pp. 50-73
    • Lai, T.L.1    Robbins, H.2
  • 28
    • 0018190841 scopus 로고
    • Strong consistency of least squares estimates in multiple regression
    • Lai, T. L., Robbins, H. and Wei, C. Z. (1978). Strong consistency of least squares estimates in multiple regression. Proc. Natl. Acad. Sci. USA 75, 3034-3036.
    • (1978) Proc. Natl. Acad. Sci. USA , vol.75 , pp. 3034-3036
    • Lai, T.L.1    Robbins, H.2    Wei, C.Z.3
  • 29
    • 49249142146 scopus 로고
    • Strong consistency of least squares estimates in multiple regression II
    • Lai, T. L., Robbins, H. and Wei, C. Z. (1979). Strong consistency of least squares estimates in multiple regression II. J. Multivariate Anal. 9, 343-361.
    • (1979) J. Multivariate Anal. , vol.9 , pp. 343-361
    • Lai, T.L.1    Robbins, H.2    Wei, C.Z.3
  • 30
    • 0001297206 scopus 로고
    • A law of the iterated logarithm for double arrays of independent random variables with applications to regression and time series models
    • Lai, T. L. and Wei, C. Z. (1982a). A law of the iterated logarithm for double arrays of independent random variables with applications to regression and time series models. Ann. Probab. 10, 320-335.
    • (1982) Ann. Probab. , vol.10 , pp. 320-335
    • Lai, T.L.1    Wei, C.Z.2
  • 31
    • 0000258837 scopus 로고
    • Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems
    • Lai, T. L. and Wei, C. Z. (1982b). Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Ann. Statist. 10, 154-166.
    • (1982) Ann. Statist. , vol.10 , pp. 154-166
    • Lai, T.L.1    Wei, C.Z.2
  • 32
    • 0011596462 scopus 로고
    • Asymptotic properties of projections with applications to stochastic regression problems
    • Lai, T. L. and Wei, C. Z. (1982c). Asymptotic properties of projections with applications to stochastic regression problems. J. Multivariate Anal. 12, 346-370.
    • (1982) J. Multivariate Anal. , vol.12 , pp. 346-370
    • Lai, T.L.1    Wei, C.Z.2
  • 33
    • 0007325849 scopus 로고
    • Lacunary systems and generalized linear processes
    • Lai, T. L. and Wei, C. Z. (1983a). Lacunary systems and generalized linear processes. Stoch. Proc. Appl. 14, 187-199.
    • (1983) Stoch. Proc. Appl. , vol.14 , pp. 187-199
    • Lai, T.L.1    Wei, C.Z.2
  • 34
    • 0003011399 scopus 로고
    • Asymptotic properties of general autoregressive models and strong consistency of least squares estimates of their parameters
    • Lai, T. L. and Wei, C. Z. (1983b). Asymptotic properties of general autoregressive models and strong consistency of least squares estimates of their parameters. J. Multivariate Anal. 13, 1-23.
    • (1983) J. Multivariate Anal. , vol.13 , pp. 1-23
    • Lai, T.L.1    Wei, C.Z.2
  • 35
    • 33750992377 scopus 로고
    • Moment inequalities with applications to regression and time series models
    • (Edited by Y. L. Tong). Monograph Series, Institute of Mathematical Statistics
    • Lai, T. L. and Wei, C. Z. (1984). Moment inequalities with applications to regression and time series models. In Inequalities in Statistics and Probability (Edited by Y. L. Tong), 165-172. Monograph Series, Institute of Mathematical Statistics.
    • (1984) Inequalities in Statistics and Probability , pp. 165-172
    • Lai, T.L.1    Wei, C.Z.2
  • 36
    • 33750968386 scopus 로고
    • Orthonormal Banach systems with applications to linear processes
    • Lai, T. L. and Wei, C. Z. (1985). Orthonormal Banach systems with applications to linear processes. Z. Wahrsch. Verw. Gebiete 70, 381-393.
    • (1985) Z. Wahrsch. Verw. Gebiete , vol.70 , pp. 381-393
    • Lai, T.L.1    Wei, C.Z.2
  • 37
    • 0001736578 scopus 로고
    • Extended least squares and their applications to adaptive control and prediction in linear systems
    • Lai, T. L. and Wei, C. Z. (1986a). Extended least squares and their applications to adaptive control and prediction in linear systems. IEEE Trans. Automat. Control 31, 898-906.
    • (1986) IEEE Trans. Automat. Control , vol.31 , pp. 898-906
    • Lai, T.L.1    Wei, C.Z.2
  • 38
    • 1542609106 scopus 로고
    • On the concept of excitation in least squares identication and adaptive control
    • Lai, T. L. and Wei, C. Z. (1986b). On the concept of excitation in least squares identication and adaptive control. Stochastics 16, 227-254.
    • (1986) Stochastics , vol.16 , pp. 227-254
    • Lai, T.L.1    Wei, C.Z.2
  • 39
    • 0023306354 scopus 로고
    • Asymptotically efficient self-tuning regulators
    • Lai, T. L. and Wei, C. Z. (1987). Asymptotically efficient self-tuning regulators. SIAM J. Contr. Optim. 25.
    • (1987) SIAM J. Contr. Optim. , vol.25
    • Lai, T.L.1    Wei, C.Z.2
  • 40
    • 0026219325 scopus 로고
    • Parallel recursive algorithms in asymptotically efficient adaptive control of linear stochastic systems
    • Lai, T. L. and Ying, Z. (1991a). Parallel recursive algorithms in asymptotically efficient adaptive control of linear stochastic systems. SIAM J. Control Optim. 29, 1091-1127.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 1091-1127
    • Lai, T.L.1    Ying, Z.2
  • 41
    • 0026218830 scopus 로고
    • Recursive identification and adaptive prediction in linear stochastic systems
    • Lai, T. L. and Ying, Z. (1991b). Recursive identification and adaptive prediction in linear stochastic systems. SIAM J. Control Optim. 29, 1061-1190.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 1061-1190
    • Lai, T.L.1    Ying, Z.2
  • 42
    • 0026817478 scopus 로고
    • Recursive solutions of estimating equations and adaptive spectral factorization
    • Lai, T. L. and Ying, Z. (1992). Recursive solutions of estimating equations and adaptive spectral factorization. IEEE Trans. Automat. Control 37, 240-243.
    • (1992) IEEE Trans. Automat. Control , vol.37 , pp. 240-243
    • Lai, T.L.1    Ying, Z.2
  • 43
    • 0017526570 scopus 로고
    • Analysis of recursive stochastic algorithms
    • Ljung, L. (1977). Analysis of recursive stochastic algorithms. IEEE Trans. Automat. Control 22, 551-575.
    • (1977) IEEE Trans. Automat. Control , vol.22 , pp. 551-575
    • Ljung, L.1
  • 45
    • 70350324901 scopus 로고
    • Robustness in time series and estimating ARMA models
    • (Edited by E. J. Hannan, P. R. Krishnaiah and M. M. Rao). North Holland, Amsterdam
    • Martin, R. D. and Yohai, V. J. (1985). Robustness in time series and estimating ARMA models. In Handbook of Statistics 5 (Edited by E. J. Hannan, P. R. Krishnaiah and M. M. Rao), 119-155. North Holland, Amsterdam.
    • (1985) Handbook of Statistics , vol.5 , pp. 119-155
    • Martin, R.D.1    Yohai, V.J.2
  • 46
    • 0000285811 scopus 로고
    • Moment inequalities and strong laws of large numbers
    • Móricz, F. (1976). Moment inequalities and strong laws of large numbers. Z. Wahrsch. Verw. Gebiete 35, 299-314.
    • (1976) Z. Wahrsch. Verw. Gebiete , vol.35 , pp. 299-314
    • Móricz, F.1
  • 48
    • 0000464775 scopus 로고
    • The multiperiod control problem under uncertainty
    • Prescott, E. C. (1972). The multiperiod control problem under uncertainty. Econometrica 40, 1043-1058.
    • (1972) Econometrica , vol.40 , pp. 1043-1058
    • Prescott, E.C.1
  • 49
    • 0002686402 scopus 로고
    • A convergence theorem for nonnegative lamost supermartingales and some applications
    • (Edited by J. Rustagi). Academic Press, New York
    • Robbins, H. and Siegmund, D. (1970). A convergence theorem for nonnegative lamost supermartingales and some applications. In Optimizing Methods in Statistics (Edited by J. Rustagi), 233-257. Academic Press, New York.
    • (1970) Optimizing Methods in Statistics , pp. 233-257
    • Robbins, H.1    Siegmund, D.2
  • 50
  • 51
    • 0000826517 scopus 로고
    • Efficient nonparametric testing and estimation
    • Univ. California Press
    • Stein, C. (1956). Efficient nonparametric testing and estimation. Proc. Third Berkeley Symp. Math. Statist. Probab. 1, 187-196. Univ. California Press.
    • (1956) Proc. Third Berkeley Symp. Math. Statist. Probab. , vol.1 , pp. 187-196
    • Stein, C.1
  • 52
    • 0002563259 scopus 로고
    • Factorization of the covariance generating function of a pure moving average process
    • Tunnicliffe-Wilson, G. (1979). Factorization of the covariance generating function of a pure moving average process. SIAM J. Numer. Anal. 6, 1-7.
    • (1979) SIAM J. Numer. Anal. , vol.6 , pp. 1-7
    • Tunnicliffe-Wilson, G.1
  • 54
    • 0001195757 scopus 로고
    • Asymptotic properties of least squares estimates in stochastic regression models
    • Wei, C. Z. (1985). Asymptotic properties of least squares estimates in stochastic regression models. Ann. Statist. 13, 1498-1508.
    • (1985) Ann. Statist. , vol.13 , pp. 1498-1508
    • Wei, C.Z.1
  • 55
    • 0000221062 scopus 로고
    • Multivariate adaptive stochastic approximation
    • Wei, C. Z. (1987a). Multivariate adaptive stochastic approximation. Ann. Statist. 15, 1115-1130.
    • (1987) Ann. Statist. , vol.15 , pp. 1115-1130
    • Wei, C.Z.1
  • 56
    • 0001732503 scopus 로고
    • Adaptive prediction by least squares predictors in stochastic regression models with applications to time series
    • Wei, C. Z. (1987b). Adaptive prediction by least squares predictors in stochastic regression models with applications to time series. Ann. Statist. 15, 1667-1682.
    • (1987) Ann. Statist. , vol.15 , pp. 1667-1682
    • Wei, C.Z.1
  • 57
    • 0006250951 scopus 로고    scopus 로고
    • Learning by doing and the value of experimentation
    • Wieland, V. (2000). Learning by doing and the value of experimentation. J. Econom. Dynam. Control 24, 501-534.
    • (2000) J. Econom. Dynam. Control , vol.24 , pp. 501-534
    • Wieland, V.1


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