Estimation with multivariate outcomes having nonignorable item nonresponse

Lyu Ni and Jun Shao ()
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Lyu Ni: East China Normal University
Jun Shao: East China Normal University

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 1, No 1, 15 pages

Abstract: Abstract To estimate unknown population parameters based on $${\varvec{y}}$$ y , a vector of multivariate outcomes having nonignorable item nonresponse that directly depends on $${\varvec{y}}$$ y , we propose an innovative inverse propensity weighting approach when the joint distribution of $${\varvec{y}}$$ y and associated covariate $${\varvec{x}}$$ x is nonparametric and the nonresponse probability conditional on $${\varvec{y}}$$ y and $${\varvec{x}}$$ x has a parametric form. To deal with the identifiability issue, we utilize a nonresponse instrument $${\varvec{z}}$$ z , an auxiliary variable related to $${\varvec{y}}$$ y but not related to the nonresponse probability conditional on $${\varvec{y}}$$ y and $${\varvec{x}}$$ 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.

Keywords: Generalized method of moments; Item nonresponse; Inverse propensity weighting; Multivariate outcome; Nonresponse instrument (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-022-00836-4

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