Review Articles

Pseudo likelihood and dimension reduction for data with nonignorable nonresponse

Ji Chen ,

School of Statistics, East China Normal University, Shanghai, China

jaechen3@126.com

Bingying Xie ,

Department of Statistics, University of Wisconsin-Madison, Madison, WI, United states

Jun Shao

School of Statistics, East China Normal University, Shanghai, China; Department of Statistics, University of Wisconsin-Madison, Madison, WI, United states

Pages 196-205 | Received 22 Jul. 2021, Accepted 22 Jul. 2021, Published online: 22 Jul. 2021,
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ABSTRACT

Tang et al. (2003. Analysis of multivariate missing data with nonignorable nonresponse. Biometrika90(4), 747–764) and Zhao & Shao (2015. Semiparametric pseudo-likelihoods in generalized linear models with nonignorable missing data. Journal of the American Statistical Association110(512), 1577–1590) proposed a pseudo likelihood approach to estimate unknown parameters in a parametric density of a response Y conditioned on a vector of covariate X, where Y is subjected to nonignorable nonersponse, X is always observed, and the propensity of whether or not Y is observed conditioned on Y and X is completely unspecified. To identify parameters, Zhao & Shao (2015. Semiparametric pseudo-likelihoods in generalized linear models with nonignorable missing data. Journal of the American Statistical Association110(512), 1577–1590) assumed that X can be decomposed into U and Z, where Z can be excluded from the propensity but is related with Y even conditioned on U. The pseudo likelihood involves the estimation of the joint density of U and Z. When this density is estimated nonparametrically, in this paper we apply sufficient dimension reduction to reduce the dimension of U for efficient estimation. Consistency and asymptotic normality of the proposed estimators are established. Simulation results are presented to study the finite sample performance of the proposed estimators.