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The strong pointwise convergence of nearest neighbor function fitting algorithm with applications to system identification. (English) Zbl 0579.93062
A nonparametric algorithm for recovering a real-valued function measured with a noise at nonrandomly chosen points of the domain is proposed. The algorithm is based on the k-nearest neighbor rule. Sufficient conditions for strong pointwise convergence are derived. An application of the algorithm to the identification of a step response of a linear dynamical system is presented.
Reviewer: A.Krzyzak

MSC:
93E12 Identification in stochastic control theory
62G05 Nonparametric estimation
65C99 Probabilistic methods, stochastic differential equations
93C05 Linear systems in control theory
93E25 Computational methods in stochastic control (MSC2010)
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References:
[1] J. Benedetti: On the nonparametric estimation of regression function. J. Roy. Statist. Soc. B39 (1977), 248-253. · Zbl 0367.62088
[2] A. A. Georgiev: Nonparametric system identification by kernel methods. IEEE Trans. Automat. Control AC-29 (1984), 356-358. · Zbl 0532.93064
[3] A. A. Georgiev: A nonparametric algorithm for identification of linear dynamic SISO systems of unknown order. Systems & Control Letters 4 (1984), 273-280. · Zbl 0601.93054
[4] A. A. Georgiev: Nonparametric kernel algorithm for recovery of functions from noisy measurements with applications. IEEE Trans. Automat. Control AC-30 (1985), to appear. · Zbl 0564.93071
[5] G. C. Goodwin, P. L. Payne: Dynamical System Identification: Experiment Design and Data Analysis. Academic Press, New York 1977. · Zbl 0578.93060
[6] W. Greblicki: Nonparametric system identification by orthogonal series. Problems Control Inform. Theory, (1979), 67-73. · Zbl 0407.93057
[7] W. Greblicki: Nearest Neighbor Algorithm for Recovering Functions from Noise. Report No. 30/82/1-6, Technical University of Wroclaw, Wroclaw 1982.
[8] W. Greblicki, A. Krzyżak: Nonparametric identification of a memoryless system with cascade structure. Internal. J. System Sci. 10 (1979), 1301 - 1310. · Zbl 0416.93017
[9] R. L. Kashyap: Maximum likelihood identification of stochastic linear systems. IEEE Trans. Automat. Control AC-15 (1970), 25-34.
[10] M. B. Priestley, M. T. Chao: Nonparametric function fitting. J. Roy. Statist. Soc. B 34 (1972), 385-392. · Zbl 0263.62044
[11] W. E. Pruitt: Summability of independent random variables. J. Math. Mech. 75 (1966), 769-776. · Zbl 0158.36403
[12] E. Rafajłowicz: Nonparametric algorithm for identification of weakly nonlinear static distributed-parameter svstems. Systems & Control Letters 4 (1984), 91 - 96.
[13] L. Rutkowski: On system identification by nonparametric function fitting. IEEE Trans. Automat. Control. AC-27 (1982), 225-227. · Zbl 0471.93065
[14] L. Rutkowski: On nonparametric identification with prediction of time-varying systems. IEEE Trans. Automat. Control AC-29 (1984), 58 - 60. · Zbl 0547.93071
[15] G. N. Saridis Z. J. Nicolic, K. S. Fu: Stochastic approximation for system identification, estimation, and decomposition of mixtures. IEEE Trans. Syst. Sci. Cybern. SSC-5 (1969), 8-15. · Zbl 0184.21801
[16] G. N. Saridis: Expanding subinterval random search for system identification and control. IEEE Trans. Automat. Control. AC-22 (1977), 405-412. · Zbl 0354.93024
[17] E. F. Schuster, S. Yakowitz: Contributions to the theory of nonparametric regression with application to system identification. Ann. Statist. 7 (1979). 139- 149. · Zbl 0401.62033
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