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Kalman-Type Filters Approach for Some Nonparametric Estimation Problems

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Stochastic Theory and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 280))

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Abstract

Some results on Kalman-type filters for nonparametric estimation problems are presented. On-line recursive filters are proposed for an estimation of a signal and it’s derivatives observed in Gaussian white noise and for a regression estimation with equidistant observation design.

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References

  1. Chow, P.-L., Khasminskii, R., and Liptser, R. Sh. (1977) Tracking of signal and its derivatives in Gaussian white noise, Stochastic Processes and Applications 69, pp. 259–273.

    Article  MathSciNet  Google Scholar 

  2. Chow, P.-L., Ibragimov I., and Khasminskii, R. (1999) Statistical approach to some ill-posed problems for linear partial differential equations. Probab. Theory Relat. Fields, 113, pp. 421–441.

    Article  MATH  MathSciNet  Google Scholar 

  3. Chow, P.-L., Khasminskii, R., and Liptser, R. Sh. (2001) On estimation of time dependent spatial signal in Gaussian white noise, Stochastic Processes and Applications, 96, pp.161–175.

    Article  MATH  MathSciNet  Google Scholar 

  4. Ibragimov, I. and Khasminskii, R. (1980) On nonparametrical regression estimation, Soviet Math. Doklady, 252, No 4, pp.780–784.

    MathSciNet  Google Scholar 

  5. Ibragimov, I. and Khasminskii, R. (1980) Estimation of signal, its derivatives, and point of maximum for Gaussian distributions. Theory of Probab. Appl., 15, pp. 703–720.

    Google Scholar 

  6. Ibragimov, I. and Khasminskii, R. (1981) Asymptotic quality bounds for regression estimation in L p, Zap. Nauchn. Sem. LOMI, 97, pp.88–101 (In Russian).

    MathSciNet  Google Scholar 

  7. Ibragimov, I. and Khasminskii, R. Statistical estimation: Asymptotic theory. Springer Verlag, 1981.

    Google Scholar 

  8. Khasminskii, R. and Liptser, R. Sh. (2001) On-line estimation of a smooth regression function, submitted to Theory of Probab. Appl.

    Google Scholar 

  9. Nussbaum, M. (1983) Optimal filtration of a function of many variables in white Gaussian noise. Problems Inform. Transmission, 19,2, pp. 23–29.

    MathSciNet  Google Scholar 

  10. Parzen, E. (1962) On estimation of a probability density function and mode. Ann. Math. Statist., 33, No 3, pp. 1065–1073.

    Article  MATH  MathSciNet  Google Scholar 

  11. Pinsker, M. (1980) Optimal filtration of square-integrable signals in Gaussian noise, Problems Inform. Transmission, 16, pp. 52–68.

    MathSciNet  Google Scholar 

  12. Rosenblatt, M. (1956) Remarks on some nonparametric estimates of a density function. Ann. Math. Statist., 27, No 3, pp. 832–837.

    Article  MATH  MathSciNet  Google Scholar 

  13. Stone, C. (1980) Optimal rates of convergence for nonparametric estimators, Ann. Statist., 8, pp. 1348–1360.

    Article  MATH  MathSciNet  Google Scholar 

  14. Stone, C. (1982) Optimal global rates of convergence for nonparametric regression, Ann. Statist., 10, pp. 1040–1053.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Wayne State University, Detroit, MI, 48202, USA

    R. Khasminskii

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  1. R. Khasminskii
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Editor information

Editors and Affiliations

  1. Dep. of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS, 66045, USA

    Bozenna Pasik-Duncan

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© 2002 Springer-Verlag Berlin Heidelberg

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Khasminskii, R. (2002). Kalman-Type Filters Approach for Some Nonparametric Estimation Problems. In: Pasik-Duncan, B. (eds) Stochastic Theory and Control. Lecture Notes in Control and Information Sciences, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48022-6_17

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  • DOI: https://doi.org/10.1007/3-540-48022-6_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43777-2

  • Online ISBN: 978-3-540-48022-8

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