Empirical likelihood inference for semi-parametric estimating equations

Qin and Lawless (1994) established the statistical inference theory for the empirical likelihood of the general estimating equations. However, in many practical problems, some unknown functional parts h(t) appear in the corresponding estimating equations E F G(X, h(T), β) = 0. In this paper, the empirical likelihood inference of combining information about unknown parameters and distribution function through the semi-parametric estimating equations are developed, and the corresponding Wilk's Theorem is established. The simulations of several useful models are conducted to compare the finite-sample performance of the proposed method and that of the normal approximation based method. An illustrated real example is also presented.