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Uniform properties of the local maximum likelihood estimate

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Abstract

Consideration was given to the properties of the local maximum likelihood estimate for the generalized regression model. The local-parameter uniform confidence belt for the regression function was constructed with their aid.

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References

  1. Katkovnik, V.Ya., Linear and Nonlinear Methods of Nonparametric Regression Analysis, Sov. Autom. Control, 1979, vol. 5, pp. 25–34.

    Google Scholar 

  2. Katkovnik, V.Ya., Nonparametric Identification and Data Smoothing. Method of Local Approximation, in Teoreticheskie osnovy tekhnicheskoi kibernetiki (Theoretical Fundamentals of Technical Cybernetics), Moscow: Nauka, 1985.

    Google Scholar 

  3. Tsybakov, A.B., Robust Restoration of Functions by Local Approximation, Probl. Peredachi Inf., 1986, vol. 22, no. 2, pp. 69–84.

    MathSciNet  Google Scholar 

  4. Fan, J., Farmen, M., and Gijbels, I., Local Maximum Likelihood Estimation and Inference, J. R. Statist. Soc. B, 1998, vol. 60, no. 3, pp. 591–608.

    Article  MathSciNet  MATH  Google Scholar 

  5. Loader, C., Local Regression and Likelihood, Springer Series in Statistics and Computing, New York: Springer, 1999.

    MATH  Google Scholar 

  6. Spokoiny, V., Wang, W., and Härdle, W., Local Quantile Regression, J. Statist. Planning Inference, 2013, vol. 143, no. 7, pp. 1109–1129.

    Article  Google Scholar 

  7. Spokoiny, V. and Vial, C., Parameter Tuning in Pointwise Adaptation Using a Propagation Approach, Ann. Statist., 2009, vol. 37, no. 5B, pp. 2783–2807.

    Article  MathSciNet  MATH  Google Scholar 

  8. Lepsky, O.V., Mammen, E., and Spokoiny, V.G., Optimal Spatial Adaptation to Inhomogeneous Smoothness: An Approach Based on Kernel Estimates with Variable Bandwidth Selectors, Ann. Statist., 1997, vol. 25, no. 3, pp. 929–947.

    Article  MathSciNet  Google Scholar 

  9. Spokoiny, V., Parametric Estimation. Finite Sample Theory, Ann. Statist., 2012, vol. 40, no. 6, pp. 2877–2909.

    Article  MathSciNet  Google Scholar 

  10. Einmahl, U. and Mason, D.M., Uniform in Bandwidth Consistency of Kernel-type Function Estimators, Ann. Statist., 2005, vol. 33, no. 3, pp. 1380–1403.

    Article  MathSciNet  MATH  Google Scholar 

  11. Dony, J., Einmahl, U., and Mason, D.M., Uniform in Bandwidth Consistency of Local Polynomial Regression Function Estimators, Austr. J. Stat., 2006, vol. 35, nos. 2–3, pp. 105–120.

    Google Scholar 

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    M. M. Zhilova & V. G. Spokoiny

  2. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russia

    M. M. Zhilova & V. G. Spokoiny

  3. Humboldt University of Berlin, Berlin, Germany

    V. G. Spokoiny

Authors
  1. M. M. Zhilova
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  2. V. G. Spokoiny
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Original Russian Text © M.M. Zhilova, V.G. Spokoiny, 2013, published in Avtomatika i Telemekhanika, 2013, No. 10, pp. 68–85.

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Zhilova, M.M., Spokoiny, V.G. Uniform properties of the local maximum likelihood estimate. Autom Remote Control 74, 1656–1669 (2013). https://doi.org/10.1134/S0005117913100068

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  • DOI: https://doi.org/10.1134/S0005117913100068

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