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 variable in distribution after the nuisance parameters are profiled away. A data simulation is also conducted.
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