An improvement on the efficiency of complete-case-analysis with nonignorable missing covariate data
- PDF / 327,653 Bytes
- 16 Pages / 439.37 x 666.142 pts Page_size
- 99 Downloads / 177 Views
An improvement on the efficiency of complete-case-analysis with nonignorable missing covariate data Jing Sun1 Received: 24 January 2019 / Accepted: 30 January 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper develops a weighted composite quantile regression method for linear models where some covariates are missing not at random but the missingness is conditionally independent of the response variable. It is known that complete case analysis (CCA) is valid under these missingness assumptions. By fully utilizing the information from incomplete data, empirical likelihood-based weights are obtained to conduct the weighted composite quantile regression. Theoretical results show that the proposed estimator is more efficient than the CCA one if the probability of missingness on the fully observed variables is correctly specified. Besides, the proposed algorithm is computationally simple and easy to implement. The methodology is illustrated on simulated data and a real data set. Keywords Missing covariates · Missing not at random · Conditionally independent · Empirical likelihood · Composite quantile regression
1 Introduction Composite quantile regression (CQR) can construct robust estimates with high efficiency via combining information from multiple quantiles as well as inheriting the robustness property from quantile regression (Zou and Yuan 2008). Owing to its advantages, CQR has become a reliable alternative to classical least squares regression in recent years. In particular, it has been widely used to handle missing covariate data problems, which are common in clinical studies and survey sampling. See Ning and Tang (2014), Sun and Sun (2015), Sun and Ma (2017), Tang and Zhou (2015) for discussions. When covariates are missing at random (MAR), Ning and Tang (2014), Tang and Zhou (2015) proposed inverse probability weighted (IPW) CQR for general linear
B 1
Jing Sun [email protected] School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China
123
J. Sun
models and varying-coefficient models respectively. Inspired by Sun et al. (2013), Zhao and Xiao (2014), Sun and Sun (2015) introduced optimal weighted quantile average estimators of the coefficient functions in varying-coefficient models when covariates are MAR, which significantly improved estimation efficiency compared with (Tang and Zhou 2015). Since Ning and Tang (2014) didn’t make full use of the observed information from incomplete cases, (Sun and Ma 2017) further incorporated the unbiased estimating equations of incomplete observations into empirical likelihood (EL) and obtained the adjusted weights for CQR, which refined the results of (Ning and Tang 2014). Moreover, although research has been done on weighted CQR methods (Bradic et al. 2011; Jiang et al. 2012; Sun et al. 2013; Zhao and Xiao 2014), Bloznelis et al. (2019) showed, for the first time, that optimality results for plug-in versions of the theoretically optimal weights may not hold any more, and thus estimated optimal weights
Data Loading...
