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Ukrainian Mathematical Journal

, Volume 66, Issue 12, pp 1823–1841 | Cite as

Corrected T(q)-Likelihood Estimator in a Generalized Linear Structural Regression Model with Measurement Errors

  • A. V. Savchenko
Article
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We study a generalized linear structural regression model with measurement errors. The dispersion parameter is assumed to be known. The corrected T (q) -likelihood estimator for the regression coefficients is constructed. In the case where q depends on the sample size and approaches 1 as the sample size infinitely increases, we establish sufficient conditions or the strong consistency and asymptotic normality of the estimator.

Keywords

Maximum Likelihood Estimator Likelihood Estimator Asymptotic Normality Dispersion Parameter Strong Consistency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. Kukush and H. Schneeweiss, “Comparing different estimators in a nonlinear measurement error model. I,” Math. Meth. Statist., 14, No. 1, 53–79 (2005).MathSciNetGoogle Scholar
  2. 2.
    H. Schneeweiss and A. Kukush, “Comparing the efficiency of structural and functional methods in measurement error models,” Theory Prob. Math. Stat., 80, 119–129 (2009).Google Scholar
  3. 3.
    C.-L. Cheng and H. Schneeweiss, “Polynomial regression with errors in the variables,” J. R. Statist. Soc. B, 60, 189–199 (1998).zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Kukush, I. Markovsky, and S. Van Huffel, “Consistent adjusted least squares estimator for errors-in-variables model AXB = C ,” Metrika, 57, No. 3, 253–285 (2003).MathSciNetGoogle Scholar
  5. 5.
    D. Ferrari and Y. Yang, “Maximum Lq -likelihood estimation,” Ann. Statist., 38, No. 2, 753–783 (2010).zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    N. Kolev, “Maximum T (q) -likelihood estimation: a new method and its application in risk management,” in: Actuarial Sci. & Finance: Proc. 6th Conf. (Samos, Greece, June 3–6, 2010), Samos (2010), p. 22.Google Scholar
  7. 7.
    A. V. Savchenko, “A corrected T (q) -likelihood estimator for the exponential structural model with measurement errors, ” Theory Probab. Math. Stat., 86, 183–192 (2013).Google Scholar
  8. 8.
    R. J. Carroll, D. Ruppert, L. A. Stefanski, and C. Crainiceanu, Measurement Error in Nonlinear Models: a Modern Perspective, Chapman & Hall, London; New York (2006).Google Scholar
  9. 9.
    C.-L. Cheng and J. W. Van Ness, Statistical Regression with Measurement Error, Arnold Publ., London (1999).zbMATHGoogle Scholar
  10. 10.
    A. Savchenko, “Modified maximum likelihood estimator in the Poisson structural model with measurement error,” in: Bull. of the Shevchenko Kyiv National University. Series: Mechanics and Mathematics [in Ukrainian], 28 (2012), pp. 26–31.Google Scholar
  11. 11.
    O. S. Usol’tseva, “A consistent estimator in the accelerated failure-time model with censored observations and measurement errors,” Theory Probab. Math. Stat., 82, 161–169 (2011).zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    A. Shiryaev, Probability [in Russian], Part 1, MCNMO, Moscow (2004).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. V. Savchenko
    • 1
  1. 1.Eastern Ukraine State UniversityIrpin’Ukraine

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