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On Existence of Explicit Asymptotically Normal Estimators in Nonlinear Regression Problems

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Analytical Methods in Statistics (AMISTAT 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 193))

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Abstract

Explicit asymptotically normal estimators for two new classes of nonlinear regression problems are constructed. The survey of such estimators and of methods for their construction is presented. Several new properties of previously established estimators are found.

This work is supported by the RFBR-grant #15-01-07460a.

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References

  1. Sakhanenko, A.I., Linke, Y.Y.: Asymptotically normal estimation of a parameter in a linear-fractional regression problem. Sib. Math. J. 41, 125–137 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Demidenko, E.: Optimization and Regression. Nauka, Moscow (1989)

    MATH  Google Scholar 

  3. Yermolenko, X.V., Sakhanenko, A.I.: Explicit asymptotically normal estimators of an unknown parameter in a partially linear regression problem. Sib. Electron. Math. Reports 10, 719–726 (2013)

    MATH  Google Scholar 

  4. Savinkina, E.N., Sakhanenko, A.I.: Explicit estimators of an unknown parameter in a power regression problem. Sib. Electron. Math. Reports 11, 725–733 (2014)

    MATH  Google Scholar 

  5. Kalenchuk, A.A., Sakhanenko, A.I.: The existence of explicit asymptotically normal estimators of an unknown parameter in a logarithmic regression problem. Sib. Electron. Math. Reports 12, 874–883 (2015)

    MATH  Google Scholar 

  6. Heyde, C.C.: Quasy-Likelihood and Its Application: A General Approach to Optimal Parameter Estimation. Springer, New York (1997)

    Google Scholar 

  7. Seber, G.A.F., Wild, C.J.: Nonlinear Regression. Wiley, New York (2003)

    Google Scholar 

  8. Janssen, P., Jureckova, J., Veraverbeke, N.: Rate of convergence of one- and two-step M-estimators with applications to maximum likelihood and Pitman estimators. Ann. Statist. 13, 1222–1229 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Verrill, S.: Rate of convergence of k-step Newton estimators to efficient likelihood estimators. Stat. Probab. Lett. 77, 1371–1376 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sakhanenko, A.I., Linke, Y.Y.: Asymptotically normal estimation of a multidimensional parameter in the linear-fractional regression problem. Sib. Math. J. 42, 317–331 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sakhanenko, A.I., Linke, Y.Y.: Asymptotically normal explicit estimation of parameters in the Michaelis – Menten equation. Sib. Math. J. 42, 517–536 (2001)

    Article  MATH  Google Scholar 

  12. Michaelis, L., Menten, M.L.: Die Kinetik der Invertinwirkung. Biochem Z 49, 333–369 (1913)

    Google Scholar 

  13. Cornish-Bowden, A.: Fundamentals of Enzyme Kinetics. Butterworth, London (1979)

    Google Scholar 

  14. Ovcharenko, S.S., Sakhanenko, A.I.: Inconsistency of estimator of Johansen and Lumry for parameters of Michaelis - Menten equation. Vestnik Yugra State Univ. 8, 95–99 (2008)

    Google Scholar 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Koptuga prospekt 4, Novosibirsk, 630090, Russia

    Alexander Sakhanenko

Authors
  1. Alexander Sakhanenko
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Correspondence to Alexander Sakhanenko .

Editor information

Editors and Affiliations

  1. Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic

    Jaromír Antoch

  2. Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic

    Jana Jurečková

  3. Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic

    Matúš Maciak

  4. Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic

    Michal Pešta

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Sakhanenko, A. (2017). On Existence of Explicit Asymptotically Normal Estimators in Nonlinear Regression Problems. In: Antoch, J., Jurečková, J., Maciak, M., Pešta, M. (eds) Analytical Methods in Statistics. AMISTAT 2015. Springer Proceedings in Mathematics & Statistics, vol 193. Springer, Cham. https://doi.org/10.1007/978-3-319-51313-3_8

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