TY - JOUR
T1 - Optimal pseudolikelihood estimation in the analysis of multivariate missing data with nonignorable nonresponse
AU - Zhao, Jiwei
AU - Ma, Yanyuan
N1 - Funding Information:
We thank the editor, associate editor and three referees for their constructive comments, which have led to a significantly improved paper. This work was partially supported by the National Center for Advancing Translational Sciences of the U.S. National Institutes of Health and the U.S. National Science Foundation.
Publisher Copyright:
© 2018 Biometrika Trust.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - Tang et al. (2003)considered a regression model with missing response, where the missingness mechanism depends on the value of the response variable and hence is nonignorable. They proposed three pseudolikelihood estimators, based on different treatments of the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates this distribution parametrically, and the third estimates the distribution nonparametrically. While it is not hard to show that the second estimator is more efficient than the first,Tang et al. (2003)only conjectured that the third estimator is more efficient than the first two. In this paper, we investigate the asymptotic behaviour of the third estimator by deriving a closed-form representation of its asymptotic variance. We then prove that the third estimator is more efficient than the other two. Our result can be straightforwardly applied to missingness mechanisms that are more general than that inTang et al. (2003).
AB - Tang et al. (2003)considered a regression model with missing response, where the missingness mechanism depends on the value of the response variable and hence is nonignorable. They proposed three pseudolikelihood estimators, based on different treatments of the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates this distribution parametrically, and the third estimates the distribution nonparametrically. While it is not hard to show that the second estimator is more efficient than the first,Tang et al. (2003)only conjectured that the third estimator is more efficient than the first two. In this paper, we investigate the asymptotic behaviour of the third estimator by deriving a closed-form representation of its asymptotic variance. We then prove that the third estimator is more efficient than the other two. Our result can be straightforwardly applied to missingness mechanisms that are more general than that inTang et al. (2003).
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U2 - 10.1093/biomet/asy007
DO - 10.1093/biomet/asy007
M3 - Article
C2 - 30799873
AN - SCOPUS:85048660131
SN - 0006-3444
VL - 105
SP - 479
EP - 486
JO - Biometrika
JF - Biometrika
IS - 2
ER -