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.
Similar content being viewed by others
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)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (No. 10771017, No. 10231030) and the Key Project of Ministry of Education (No. 309007).
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-008-8805-3