Two-stage estimation and bias-corrected empirical likelihood in a partially linear single-index varying-coefficient model

The estimation and empirical likelihood (EL) of the parameters of interest in a partially linear single-index varying-coefficient model are studied. A two-stage method is presented to estimate the regression parameters and the coefficient functions. The asymptotic distributions of the proposed estimators are obtained. Meanwhile, a bias-corrected EL ratio for the regression parameters is proposed. It is shown that the ratio is asymptotically standard chi-squared. The result can be directly used to construct the EL confidence regions of the regression parameters. Simulation studies are carried out to evaluate the finite sample behaviour of the proposed method. An application example of a real data set is given.

Automated summary

This paper studies the estimation and empirical likelihood (EL) of the parameters in a partially linear single-index varying-coefficient model. A two-stage method is proposed to estimate the regression parameters and the coefficient functions. The asymptotic distributions of the proposed estimators are obtained. A bias-corrected EL ratio for the regression parameters is also proposed. It is shown that the ratio asymptotically follows a standard chi-squared distribution. The proposed method is evaluated through simulation studies and an application example using a real data set.