Jackknife empirical likelihood of error variance for partially linear varying-coefficient model with missing covariates

Abstract

In this paper, we apply the profile least-square method and inverse probability weighted method to define estimation of the error variance in partially linear varying-coefficient model when the covariates are missing at random. At the same time, we construct a jackknife estimator and jackknife empirical likelihood (JEL) statistic of the error variance, respectively. It is proved that the proposed estimators are asymptotical normality and the JEL statistic admits a limiting standard chi-square distribution. A simulation study is conducted to compare the JEL method with the normal approximation approach in terms of coverage probabilities and average interval lengths, and a comparison of the proposed estimators is done based on sample means, biases and mean square errors under different settings. Subsequently, a real data set is analyzed for illustration of the proposed methods.

Keywords:

• Asymptotically normal
• error variance
• Jackknife empirical likelihood
• missing at random
• partially linear varying-coefficient model

AMS 2000 Subject Classifications:

• Primary: 62E20
• Secondary: 62G08

Acknowledgments

The authors thank to the editor, the associate editor and two anonymous referees for their constructive comments and suggestions which led to a substantial improvement of an early manuscript.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11831008, 11971171), the China Postdoctoral Science Foundation (2019M651422), the National Social Science Foundation Key Program (17ZDA091), the 111 Project of China (B14019) and Natural Science Foundation of Shanghai (17ZR1409000).