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.
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.