Corrected T(q)-Likelihood Estimator in a Generalized Linear Structural Regression Model with Measurement Errors
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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.
KeywordsMaximum Likelihood Estimator Likelihood Estimator Asymptotic Normality Dispersion Parameter Strong Consistency
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- 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
- 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.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.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
- 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
- 12.A. Shiryaev, Probability [in Russian], Part 1, MCNMO, Moscow (2004).Google Scholar