Empirical likelihood inference for parameters in a partially linear errors-in-variables model

Abstract

In this paper, we consider the application of the empirical likelihood method to a partially linear model with measurement errors in the non-parametric part. It is shown that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. Furthermore, we obtain the maximum empirical likelihood estimate of the unknown parameter by using the empirical log-likelihood ratio function, and the resulting estimator is shown to be asymptotically normal. Some simulations and an application are conducted to illustrate the proposed method.

Keywords:

• empirical likelihood
• measurement error
• confidence regions
• coverage probability
• maximum empirical likelihood estimate

2000 Mathematics Subject Classifications :

• 62F12
• 62G05

Acknowledgements

The authors are grateful to the referees and the editor for their constructive suggestions that greatly improved the paper. This work was partially supported by the RFDP (20020027010) and the NSFC (10771017, 11026132) of China, and by the Fundamental Research Funds for the Central Universities (GK200902050) and the Excellent Preresearch Projects of Science and Technology of Shaanxi Normal University (200902010).