Asymptotic distribution theory on pseudo semiparametric maximum likelihood estimator with covariates missing not at random

摘要

Recently, Cook et al. proposed a semiparametric likelihood estimator to improve study efficiency for a kind of survival data with covariate entries missing not at random (MNAR). Readily available supplementary information on the covariate is utilized in the estimation. They assume that the conditional distributions of the covariate X that having missing entry given the completely observed covariate Z, is known. Guo et al. suggested to replace with its consistent estimator in the likelihood equation when is unknown. However, they did not derive the asymptotic theory of the resulted estimator in this case. This paper fills the gap. The theoretical development makes use of the theory of modern empirical process.