Abstract
In this paper we use profile empirical likelihood to construct confidence regions for regression coefficients in partially linear model with longitudinal data. The main contribution is that the within-subject correlation is considered to improve estimation efficiency. We suppose a semi-parametric structure for the covariances of observation errors in each subject and employ both the first order and the second order moment conditions of the observation errors to construct the estimating equations. Although there are nonparametric estimators, the empirical log-likelihood ratio statistic still tends to a standard χ 2 p variable in distribution after the nuisance parameters are profiled away. A data simulation is also conducted.
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References
Cheng, S. C., Wei, L.J. Inferences for a semiparametric model with panel data. Biometrika., 85: 967–972 (2000)
Fan, J. Li, R.Z. New estimation and model selection precedures for semiparametric modeling in longitudinal data analysis. J. Am. Statist. Assoc., 99: 710–723 (2004)
Fan, J. Gijbels, I. Data-driven bandwidth selection in local polynomial fitting: variable bandwidth a nd spatial adaptation. J. R. Statist. Soc., B57: 371–394 (1995)
Fan, J., Yao, Q. Efficient estimation of conditional variance functions in stochastic regression. Biometrika., 85: 645–660 (1998)
He, X., Zhu, Z.Y., Fung, W.K. Estimation in a semiparametric model for longitudinal data with unspecified dependence structure. Biometrika., 89: 579–590 (2002)
Hoeffding, W., Robbins, H. The central limit theorem for dependent random variables. Duke Mathematical Journal., 15: 773–780 (1948)
Hu, Z. H., Wang, N., Carroll, R.J. Profile-kernel versus backfitting in the partially linear models for longitudinal/clustered data. Biometrika., 91: 251–262 (2004)
Lin, D. Y., Ying, Z. Semiparametric and nonparametric regression analysis of longitudinal data (with discussion). J. Am. Statist. Assoc., 96: 103–126 (2001)
Lin, X. H., Carroll, R.J. Semiparametric regression for clustered data using generalized estimating equations. J. Am. Statist. Assoc., 96: 1045–1056 (2001)
Moyeed, R. A., Diggle, P.J. Rates of convergence in semiparametric modelling of longitudinal data. Aust. J. Statist., 36: 75–93 (1994)
Qin, J., Lawless, J. Empirical likelihood and general estimating equations. Ann. Statist., 22: 300–325 (1994)
Owen, A. B. Empirical likelihood ratio confidence intervals for a single function. Biometrika., 75: 237–249 (1988)
Owen, A. B. Empirical likelihood confidence regions. Ann. Statist., 18: 90–120 (1990)
Xue, L., Zhu., L. Empirical likelihood semiparametric regression analysis for longitudinal data. Biometrika., 94: 921–937 (2007)
Zeger, S. L., Diggle, P.J. Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics., 50: 689–699 (1994)
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Supported by NBRP (973 Program 2007CB814901) of China, NNSF project (10771123) of China, RFDP (20070422034) of China and NSF projects (ZR2010AZ001) of Shandong Province of China.
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Hu, S., Lin, L. Empirical likelihood analysis of longitudinal data involving within-subject correlation. Acta Math. Appl. Sin. Engl. Ser. 28, 731–744 (2012). https://doi.org/10.1007/s10255-011-0070-1
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DOI: https://doi.org/10.1007/s10255-011-0070-1