Empirical likelihood inference in mixtures of semiparametric varying coefficient EV models for longitudinal data with nonignorable dropout

In this paper, empirical likelihood inference in mixtures of semiparametric varying coefficient errors-in-variables (EV) models for longitudinal data with nonignorable dropout is investigated. The empirical log-likelihood ratio statistic for the fixed-effects parameters and the mean parameters of random effects are proposed. The proposed statistic at the true parameters is proven to be asymptotically χq+r2, where q and r are the dimensions of the fixed and random effects respectively, and the corresponding confidence regions for the parameters of interest are then constructed. We also obtain the maximum empirical likelihood estimator of the parameters, and prove that it is asymptotically normal under some suitable conditions. Simulation studies are undertaken to assess the finite sample performance of the proposed method.