A general framework for quantile estimation with incomplete data

• 成果类型: Article
• 署名作者: Han, Peisong; Kong, Linglong; Zhao, Jiwei; Zhou, Xingcai
• 署名单位: University of Michigan System; University of Michigan; University of Alberta; State University of New York (SUNY) System; University at Buffalo, SUNY; Nanjing Audit University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12309
• 发表日期: 2019
• 页码: 305-333
• 关键词: likelihood-based inference; doubly robust estimation; cd4 cell counts; empirical-likelihood; Missing Data; multiple imputation; Semiparametric Efficiency; improving efficiency; regression-models; longitudinal data

摘要

Quantile estimation has attracted significant research interest in recent years. However, there has been only a limited literature on quantile estimation in the presence of incomplete data. We propose a general framework to address this problem. Our framework combines the two widely adopted approaches for missing data analysis, the imputation approach and the inverse probability weighting approach, via the empirical likelihood method. The method proposed is capable of dealing with many different missingness settings. We mainly study three of them: estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates; estimating the conditional quantile of a fully observed response while the covariates are partially available; estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables. The method proposed allows multiple models for both the missingness probability and the data distribution. The resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified. The asymptotic distributions are established by using empirical process theory.