Two-Stage Estimation of Partially Linear Varying Coefficient Quantile Regression Model with Missing Data

In this paper, the statistical inference of the partially linear varying coefficient quantile regression model is studied under random missing responses. A two-stage estimation procedure is developed to estimate the parametric and nonparametric components involved in the model. Furthermore, the asym...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-02, Vol.12 (4), p.578
Main Authors: Luo, Shuanghua, Yan, Yuxin, Zhang, Cheng-yi
Format: Article
Language:English
Subjects:
Asymptotic properties
Chi-square test
composite quantile regression
confidence interval
Confidence intervals
Electronic data processing
empirical likelihood
Lagrange multiplier
Likelihood ratio
Mathematical research
Methods
Missing data
missing responses
partially linear varying coefficient model
Quantiles
Random variables
Regression analysis
Regression models
Statistical analysis
Statistical inference
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Summary:In this paper, the statistical inference of the partially linear varying coefficient quantile regression model is studied under random missing responses. A two-stage estimation procedure is developed to estimate the parametric and nonparametric components involved in the model. Furthermore, the asymptotic properties of the estimators obtained are established under some mild regularity conditions. In addition, the empirical log-likelihood ratio statistic based on imputation is proposed, and it is proven that this statistic obeys the standard Chi-square distribution; thus, the empirical likelihood confidence interval of the parameter component of the model is constructed. Finally, simulation results show that the proposed estimation method is feasible and effective.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12040578