Robust inference for estimating equations with nonignorably missing data based on SIR algorithm

ABSTRACT

Nonresponse is a very common phenomenon in survey sampling. Nonignorable nonresponse – that is, a response mechanism that depends on the values of the variable having nonresponse – is the most difficult type of nonresponse to handle. This article develops a robust estimation approach to estimating equations (EEs) by incorporating the modelling of nonignorably missing data, the generalized method of moments (GMM) method and the imputation of EEs via the observed data rather than the imputed missing values when some responses are subject to nonignorably missingness. Based on a particular semiparametric logistic model for nonignorable missing response, this paper proposes the modified EEs to calculate the conditional expectation under nonignorably missing data. We can apply the GMM to infer the parameters. The advantage of our method is that it replaces the non-parametric kernel-smoothing with a parametric sampling importance resampling (SIR) procedure to avoid nonparametric kernel-smoothing problems with high dimensional covariates. The proposed method is shown to be more robust than some current approaches by the simulations.

KEYWORDS:

• Estimating equation
• generalized method of moments
• nonlinear science
• nonignorable missing data
• Monte Carlo
• sampling importance resampling

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by National Natural Science Foundation of China (NNSF) project (11971265), Natural Science Foundation of Shandong Province of China (NSF) project (ZR2019MA016), Shandong Province Key Research and Development Plan (2018GSF120020), the Project of Shandong Province Higher Educational Science and Technology Program (J18KB099).