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When the response mechanism is believed to be not missing at random (NMAR), avalid analysis requires stronger assumptions on the response mechanism thanstandard statistical methods would otherwise require. Semiparametric estimatorshave been developed under the model assumptions on the response mechanism. Inthis paper, a new statistical test is proposed to guarantee modelidentifiability without using any instrumental variable. Furthermore, wedevelop optimal semiparametric estimation for parameters such as the populationmean. Specifically, we propose two semiparametric optimal estimators that donot require any model assumptions other than the response mechanism. Asymptoticproperties of the proposed estimators are discussed. An extensive simulationstudy is presented to compare with some existing methods. We present anapplication of our method using Korean Labor and Income Panel Survey data.

Semiparametric Optimal Estimation With Nonignorable Nonresponse Data