Instrumental variable-based empirical likelihood inferences for varying-coefficient models with error-prone covariates

Abstract

This paper presents the empirical likelihood inferences for a class of varying-coefficient models with error-prone covariates. We focus on the case that the covariance matrix of the measurement errors is unknown and neither repeated measurements nor validation data are available. We propose an instrumental variable-based empirical likelihood inference method and show that the proposed empirical log-likelihood ratio is asymptotically chi-squared. Then, the confidence intervals for the varying-coefficient functions are constructed. Some simulation studies and a real data application are used to assess the finite sample performance of the proposed empirical likelihood procedure.

Keywords:

• varying-coefficient models
• error-prone covariate
• empirical likelihood
• instrumental variable
• confidence intervals

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant Nos. 11171012, 11101119, and 11126332), the National Social Science Foundation of China (Grant No. 11CTJ004), the Natural Science Foundation of Guangxi (Grant No. 2010GXNSFB013051), and the Philosophy and Social sciences Foundation of Guangxi (Grant No. 11FTJ002).