Efficient inverse probability weighting method for quantile regression with nonignorable missing data

ABSTRACT

Quantitle regression (QR) is a popular approach to estimate functional relations between variables for all portions of a probability distribution. Parameter estimation in QR with missing data is one of the most challenging issues in statistics. Regression quantiles can be substantially biased when observations are subject to missingness. We study several inverse probability weighting (IPW) estimators for parameters in QR when covariates or responses are subject to missing not at random. Maximum likelihood and semiparametric likelihood methods are employed to estimate the respondent probability function. To achieve nice efficiency properties, we develop an empirical likelihood (EL) approach to QR with the auxiliary information from the calibration constraints. The proposed methods are less sensitive to misspecified missing mechanisms. Asymptotic properties of the proposed IPW estimators are shown under general settings. The efficiency gain of EL-based IPW estimator is quantified theoretically. Simulation studies and a data set on the work limitation of injured workers from Canada are used to illustrated our proposed methodologies.

KEYWORDS:

• Auxiliary information
• empirical likelihood
• inverse probability weighting
• missing not at random
• quantile regression

AMS SUBJECT CLASSIFICATION:

• 62F12
• 62H12

Acknowledgments

The authors are grateful to the Editor, an Associate Editor and two referees for constructive suggestions that greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Tang's work was supported by grants from the National Science Fund for Distinguished Young Scholars of China (11225103). Jiang's work was supported by research funds from Manitoba Health Research Council (MHRC).