A beyond multiple robust approach for missing response problem

Imputation and the inverse probability weighting are two commonly used approaches in missing data analysis. Parametric versions of them are not robust due to model misspecification of some unknown functions. Nonparametric ones are robust but are impractical when the number of covariates is large due to the problem of “curse of dimension”. A beyond multiple robust method is proposed in this paper. This method balances the parametric and nonparametric methods by using some model information contained in the outcome regression function and the selection probability function, and hence alleviates the model misspecification problem and “curse of dimension” problem simultaneously. To illustrate the proposed method, we focus on the estimating problem of response mean in the presence of missing responses. A beyond multiple robust estimator of the response mean is defined, which is proved to be consistent and asymptotically normal as long as one of the true models for the outcome regression or selection probability functions can be some function of its assumed models, without the requirement that one of the true models is correctly specified. Also, it is shown that the asymptotic variance of the proposed estimator is equal to the semiparametric efficiency bound established by Hahn (1998, Econometrica, pp 315–331) when both the selection probability function and the outcome regression function are the functions of their assumed models, respectively. The finite sample properties of the proposed estimator are evaluated by simulation studies and the proposed method is illustrated by a real data analysis.