Empirical likelihood confidence regions for semi-varying coefficient models with linear process errors

Abstract

In this paper, we apply the empirical likelihood method to semi-varying coefficient models with linear process errors, propose two empirical log-likelihood ratio statistics and show that their limiting distributions are two weighted sums of independent chi-square distributions with 1 degree of freedom. By estimating the unknown weights consistently, we not only construct the empirical likelihood confidence regions for the parametric component, but also construct the point-wise empirical likelihood confidence regions and the simultaneous empirical likelihood confidence bands for the varying-coefficient functions. Monte Carlo simulation results show that the proposed empirical likelihood confidence regions have better coverage probabilities and shorter median lengths than the normal approximation confidence regions ignoring the correlation information.