Abstract: In missing data analysis, multiple robustness is a desirable property resulting from the calibration technique. A multiply robust estimator is consistent if any one of the multiple data distribution models and missingness mechanism models is correctly specified. So far in the literature, multiple robustness has only been established when data are missing at random (MAR). We study how to carry out calibration to construct a multiply robust estimator when data are missing not at random (MNAR). With multiple models available, where each model consists of two components, one for data distribution for complete cases and one for missingness mechanism, our proposed estimator is consistent if any one pair of models are correctly specified.

Key words and phrases: Calibration, empirical likelihood, missing not at random (MNAR), multiple robustness, nonignorable nonresponse.