Abstract
This paper mainly introduces the method of empirical likelihood and its applications on two different models. We discuss the empirical likelihood inference on fixed-effect parameter in mixed-effects model with error-in-variables. We first consider a linear mixed-effects model with measurement errors in both fixed and random effects. We construct the empirical likelihood confidence regions for the fixed-effects parameters and the mean parameters of random-effects. The limiting distribution of the empirical log likelihood ratio at the true parameter is χ 2 p+q , where p, q are dimension of fixed and random effects respectively. Then we discuss empirical likelihood inference in a semi-linear error-in-variable mixed-effects model. Under certain conditions, it is shown that the empirical log likelihood ratio at the true parameter also converges to χ 2 p+q . Simulations illustrate that the proposed confidence region has a coverage probability more closer to the nominal level than normal approximation based confidence region.
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References
Azzalini, A. A note on the estimation of a distribution function and quantiles by kernel method. Bimetrika, 68: 326–328 (1981)
Chen, S.X., Cui, H.J. On the second order properties of empirical likelihood with moment restrictions. J. Econometrics, 141: 492–516 (2007)
Chen, S.X., Hall, P. Smoothed empirical likelihood confidence interval for quantiles. Ann. Statist., 21: 1166–1181 (1993)
Chen, X.R., Wu, Y.H. Consistency of L 1 estimates in censored regression models. Communications in Statistics-Theory and Methods, 23: 1847–1858 (1993)
Cui, H.J., Ng, Kai W., Zhu, L.X. Estimation in mixed effects model with errors in variables. J. Multivariate Anal., 91: 53–73 (2004)
Cui, H.J., Chen, S.X. Empirical likelihood confidence region for parameter in the error-in-variables models. J. Multivariate Anal., 84: 101–115 (2003)
Cui, H.J., Kong, E.F. Empirical likelihood confidence regions for semi-parametric errors-in-variables models. Scan. J. of Statist., 33: 153–168 (2006)
DiCicco, T., Hall, P., Romano, J. Empirical likelihood is Barterlett-correctable. Ann. of Statist., 19: 1053–1061 (1991)
Liang, H., Härdle, W., Carroll, R.J. Estimation in a semiparametric partialy linear error-in-variables model. Ann. of Statist., 27: 1519–1535 (1999)
Liang, H. Asymptotic normality of parametric part in partially linear models with measurement error in the nonparametric part. J. Statist. Planning and Inference, 86: 51–62 (2000)
Owen, A. Empirical likelihood ratio confidence regions. Ann. Statist., 18: 90–120 (1990)
Owen, A. Empirical likelihood. Chapman and Hall/CRC Press, 2001
Qin, J., Lawless, J.F. Emprical likelihood and general estimating equations. Ann. Statist., 22: 300–325 (1994)
Shi, J., Lau, T.S. Empirical likelihood for partially linear models. J. Multivariate Anal., 72: 132–148 (2000)
Zhong, X.P., Fung, W.K., Wei, B.C. Estimation in linear models with random effects and errors-in-variables. Ann. Inst. Math. Statist., 54: 595–606 (2002)
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Supported by the National Natural Science Foundation of China (No. 10771017, No. 10231030) and the Key Project of Ministry of Education (No. 309007).
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Chen, Qh., Zhong, Ps. & Cui, Hj. Empirical likelihood for mixed-effects error-in-variables model. Acta Math. Appl. Sin. Engl. Ser. 25, 561–578 (2009). https://doi.org/10.1007/s10255-008-8805-3
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DOI: https://doi.org/10.1007/s10255-008-8805-3