摘要
Tang et al. (2003. Analysis of multivariate missing data with nonignorable nonresponse.Biometrika, 90(4), 747–764) and Zhao & Shao (2015. Semiparametric pseudo-likelihoods in generalized linear models with nonignorable missing data. Journal of the American Statistical Association, 110(512), 1577–1590) proposed a pseudo likelihood approach to estimate unknownparameters in a parametric density of a response Y conditioned on a vector of covariate X, whereY is subjected to nonignorable nonersponse, X is always observed, and the propensity of whetheror 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 withnonignorable missing data. Journal of the American Statistical Association, 110(512), 1577–1590)assumed that X can be decomposed into U and Z, where Z can be excluded from the propensitybut is related with Y even conditioned on U. The pseudo likelihood involves the estimation ofthe joint density of U and Z. When this density is estimated nonparametrically, in this paper weapply sufficient dimension reduction to reduce the dimension of U for efficient estimation. Consistency and asymptotic normality of the proposed estimators are established. Simulation resultsare presented to study the finite sample performance of the proposed estimators.
基金
This work was supported by Division of Mathematical Sciences[1612873]
the Chinese Ministry of Education 111 Project[B14019].
