Empirical Likelihood for a Partially Linear Single-Index Measurement Error Model with Right-Censored Data

Abstract

This article considers the application of the empirical likelihood method to a partially linear single-index measure error model (PLSIMeM) with right-censored data. With a synthetic data approach, an empirical log-likelihood ratio statistic for the parametric components is defined and it is shown that its limiting distribution is a mixture of central chi-squared distributions. Based on this, a confidence region for the parameters is constructed. To increase the accuracy of the confidence region, we also propose an adjusted empirical log-likelihood ratio statistic for the parameters. The resulting statistic is proved to follow a standard chi-squared limiting distribution. Simulation studies are undertaken to assess the finite sample performance of the proposed confidence regions.

Keywords:

• Confidence region
• Empirical likelihood
• Measurement error model
• Partially linear single-index model
• Right censoring

Mathematics Subject Classification:

• 62G08
• 62E20

Acknowledgments

The author would like to thank Editor and referees for their truly helpful comments and suggestions which led to a much improved presentation.