Efficient empirical-likelihood-based inferences for the single-index model

This article proposes the efficient empirical-likelihood-based inferences for the single component of the parameter and the link function in the single-index model. Unlike the existing empirical likelihood procedures for the single-index model, the proposed profile empirical likelihood for the parameter is constructed by using some components of the maximum empirical likelihood estimator (MELE) based on a semiparametric efficient score. The empirical-likelihood-based inference for the link function is also considered. The resulting statistics are proved to follow a standard chi-squared limiting distribution. Simulation studies are undertaken to assess the finite sample performance of the proposed confidence intervals. An application to real data set is illustrated. (c) 2011 Elsevier Inc. All rights reserved.