Empirical likelihood for estimating equations with nonignorably missing data

Abstract

We develop an empirical likelihood (EL) inference on parameters in generalized estimating equations with nonignorably missing response data. We consider an exponential tilting model for the nonignorably missing mechanism, and propose modified estimating equations by imputing missing data through a kernel regression method. We establish some asymptotic properties of the EL estimators of the unknown parameters under different scenarios. With the use of auxiliary information, the EL estimators are statistically more efficient. Simulation studies are used to assess the finite sample performance of our proposed EL estimators. We apply our EL estimators to investigate a data set on earnings obtained from the New York Social Indicators Survey.

Semiparametric maximum likelihood estimation with data missing not at random

“…Kim & Yu () suggested a semiparametric method to estimate using a parametric response mechanism but their approach requires a validation sample to estimate the parameters in the response mechanism. Tang, Zhao, & Zhu () extended the method of Kim & Yu () to estimate more general parameters by using the technique of empirical likelihood. Zhao et al () applied the method of Qin, Leung, & Shao () to construct a ‐consistent estimator without using any validation sample.…”

A propensity score adjustment method for regression models with nonignorable missing covariates

“…Using similar arguments as given in Tang et al (2014), we can prove that Z n2j,k = o p (1) (j = 2, 3) and…”

“…According to the same arguments as given in Lemma 5 of Tang et al (2014), we have W 2 = o p (n −1/2 ) and…”

Rank-based estimating equation with non-ignorable missing responses via empirical likelihood

“…Recent progress in the EL method includes linear transformation models with right censoring ), Yang & Zhao (2012), the jackknife EL procedure (Jing et al (2009), Gong et al (2010, Zhang & Zhao (2013), ), high dimensional EL method (Chen et al (2009), Hjort et al (2009), Tang & Leng (2010, Lahiri et al (2012)), and the signedrank regression (Bindele & Zhao, 2016). More recently, in the context of missing response under the MNAR assumption, empirical likelihood approaches have been proposed by Niu et al (2014) and Tang et al (2014). Their approaches reveal that the considered empirical likelihood functions were defined based on the leastsquares estimating equation, which for many of the reasons discussed above is non robust and less efficient in many scenarios.…”