Local linear regression for generalized linear models with missing data

• 成果类型: Article
• 署名作者: Wang, CY; Wang, SJ; Gutierrez, RG; Carroll, RJ
• 署名单位: Fred Hutchinson Cancer Center; Southern Methodist University; Texas A&M University System; Texas A&M University College Station; Humboldt University of Berlin
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1028-1050
• 关键词: quasi-likelihood functions; kernel regression; disease

摘要

Fan, Heckman and Wand proposed locally weighted kernel polynomial regression methods for generalized linear models and quasilikelihood functions. When the covariate variables are missing at random, we propose a weighted estimator based on the inverse selection probability weights. Distribution theory is derived when the selection probabilities are estimated nonparametrically. We show that the asymptotic variance of the resulting nonparametric estimator of the mean function in the main regression model is the same as that when the selection probabilities are known, while the biases are generally different. This is different from results in parametric problems, where it is known that estimating weights actually decreases asymptotic variance. To reconcile the difference between the parametric and nonparametric problems, we obtain a second-order variance result for the nonparametric case. We generalize this result to local estimating equations. Finite-sample performance is examined via simulation studies. The proposed method is demonstrated via an analysis of data from a case-control study.