Weighted composite quantile regression analysis for nonignorable missing data using nonresponse instrument

ABSTRACT

Efficient statistical inference on nonignorable missing data is a challenging problem. This paper proposes a new estimation procedure based on composite quantile regression (CQR) for linear regression models with nonignorable missing data, that is applicable even with high-dimensional covariates. A parametric model is assumed for modelling response probability, which is estimated by the empirical likelihood approach. Local identifiability of the proposed strategy is guaranteed on the basis of an instrumental variable approach. A set of data-based adaptive weights constructed via an empirical likelihood method is used to weight CQR functions. The proposed method is resistant to heavy-tailed errors or outliers in the response. An adaptive penalisation method for variable selection is proposed to achieve sparsity with high-dimensional covariates. Limiting distributions of the proposed estimators are derived. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. An application to the ACTG 175 data is analysed.

KEYWORDS:

• Composite quantile regression
• local identification
• nonignorable missing data
• empirical likelihood
• variable selection

AMS SUBJECT CLASSIFICATION:

• 62G35
• 62F35
• 62F12

Acknowledgements

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

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was supported by grants from the National Natural Science Foundation of China (11225103, 11426197, 11301464, 11301465, 11501208) and the China Postdoctoral Science Foundation (2014M560317).