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October 2021 Semiparametric optimal estimation with nonignorable nonresponse data
Kosuke Morikawa, Jae Kwang Kim
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Ann. Statist. 49(5): 2991-3014 (October 2021). DOI: 10.1214/21-AOS2070

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.

Funding Statement

The research of K. Morikawa was partially supported by JSPS KAKENHI Grant-in-Aids for Early-Career Scientists (19K14592). The research of J. K. Kim was partially supported by a grant from US National Science Foundation (MMS-1733572).

Acknowledgments

The authors are grateful for the very constructive comments of the three anonymous referees and the Associate Editor.

Citation

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Kosuke Morikawa. Jae Kwang Kim. "Semiparametric optimal estimation with nonignorable nonresponse data." Ann. Statist. 49 (5) 2991 - 3014, October 2021. https://doi.org/10.1214/21-AOS2070

Information

Received: 1 May 2020; Revised: 1 March 2021; Published: October 2021
First available in Project Euclid: 12 November 2021

Digital Object Identifier: 10.1214/21-AOS2070

Subjects:
Primary: 62F35 , 62G20
Secondary: 62G10

Keywords: Estimating functions , Identification , incomplete data , not missing at random (NMAR) , semiparametric efficient estimation

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 5 • October 2021
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