Jackknife empirical likelihood for the error variance in linear errors-in-variables models with missing data

Abstract

Measurement errors and missing data are often arise in practice. Under this circumstance, we focus on using jackknife empirical likelihood (JEL) and adjust jackknife empirical likelihood (AJEL) methods to construct confidence intervals for the error variance in linear models. Based on residuals of the models, the biased-corrected inverse probability weighted estimator of the error variance is introduced. Furthermore, we propose the jackknife estimator, jackknife and adjust jackknife empirical log-likelihood ratios of the error variance and establish their asymptotic distributions. Simulation studies in terms of coverage probability and average length of confidence intervals are conducted to evaluate the proposed method. A real data set is used to illustrate the proposed JEL and AJEL methods.

Keywords:

• Confidence interval
• errors-in-variables
• error variance
• Jackknife empirical likelihood
• missing data

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions, which actually stimulated this work.

Additional information

Funding

This work is supported by the Project of Humanities and Social Science Foundation of Ministry of Education (grant no. 20YJC910003), Natural Science Foundation of Shanghai (grant no. 20ZR1423000) and Zhejiang Provincial Natural Science Foundation (grant no. LY18A010007).