Empirical likelihood inference in mixture of semiparametric varying-coefficient models for longitudinal data with non-ignorable dropout

In this paper, empirical likelihood inference in mixture of semiparametric varying-coefficient models for longitudinal data with non-ignorable dropout is investigated. We estimate the non-parametric function based on the estimating equations and the local linear profile-kernel method. An empirical log-likelihood ratio statistic for parametric components is proposed to construct confidence regions and is shown to be an asymptotically chi-squared distribution. The non-parametric version of Wilk's theorem is also derived. A simulation study is undertaken to illustrate the finite sample performance of the proposed method.