Estimation with multivariate outcomes having nonignorable item nonresponse

To estimate unknown population parameters based on y, a vector of multivariate outcomes having nonignorable item nonresponse that directly depends on y, we propose an innovative inverse propensity weighting approach when the joint distribution of y and associated covariate x is nonparametric and the nonresponse probability conditional on y and x has a parametric form. To deal with the identifiability issue, we utilize a nonresponse instrument z, an auxiliary variable related to y but not related to the nonresponse probability conditional on y and x. We utilize a modified generalized method of moments to obtain estimators of the parameters in the nonresponse probability. Simulation results are presented and an application is illustrated in a real data set.