Empirical Likelihood for Partially Linear Single-Index Errors-in-Variables Model

Abstract

In this article, we consider the application of the empirical likelihood method to a partially linear single-index model. We focus on the case where some covariates are measured with additive errors. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the proposed confidence region has coverage probability which is closer to the nominal level, as well as narrower than those of normal approximation method. A real data example is given.

Keywords:

• Confidence region
• Coverage probability
• Empirical likelihood
• Measurement error
• Partially linear single-index model

Mathematics Subject Classification:

• Primary 62G15
• Secondary 62E20

Acknowledgment

This work was partially supported by the RFDP (No: 20020027010) and NSFC (No: 10771017).