Empirical likelihood for semiparametric varying coefficient partially linear models with longitudinal data

Semivarying coefficient partially linear model is a very inclusive semiparametric model, which contains the partially linear model and varying coefficient model as its special cases. In this paper, we consider the empirical-likelihood-based inference for a semivarying coefficient partially linear model with longitudinal data. An empirical likelihood ratio statistic for the parametric components is proposed and the nonparametric version of Wilk's theorem is proved. Thus the confidence intervals/regions of the parametric component with asymptotically correct coverage probabilities can be constructed. Some simulations are studied to illustrate the finite sample performance of the proposed method.