Semiparametric optimal estimation with nonignorable nonresponse data
Kosuke Morikawa, Jae Kwang Kim
The Annals of Statistics · 2021 · Volume 49 · Issue 5
Abstract
When the response mechanism is believed to be not missing at random (NMAR), a valid analysis requires stronger assumptions on the response mechanism than standard statistical methods would otherwise require. Semiparametric estimators have been developed under the parametric model assumptions on the response mechanism. In this paper, a new statistical test is proposed to guarantee model identifiability without using instrumental variable assumption. Furthermore, we develop optimal semiparametric estimation for parameters such as the population mean. Specifically, we propose two semiparametric optimal estimators that do not require any model assumptions other than the response mechanism. Asymptotic properties of the proposed estimators are discussed. An extensive simulation study is presented to compare with some existing methods. We present an application of our method using Korean labor and income panel survey data.
Keywords
62F35, 62G10, 62G20, Estimating functions, Identification, incomplete data, not missing at random (NMAR), semiparametric efficient estimation
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