Nonparametric and Semiparametric Models for Missing Covariates in Parametric Regression
参数回归中缺失协变量的非参数与半参数模型AI 解读 ↓
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参数回归中缺失协变量的非参数与半参数模型
- 研究问题
- 在随机缺失假设下，怎样降低参数回归对协变量分布误设的敏感性，并在不同缺失模式中保持回归参数估计的一致性？
- 方法与思路
- 作者对简单缺失模式使用非参数协变量模型，对一般模式分解条件分布，以参数化优势比结合非参数其余部分构造半参数似然。
- 材料陈述的贡献
- 摘要称，简单模式可获得一致且半参数有效估计；一般模式在优势比正确时保持一致，并增强稳健性、减轻似然积分困难。
- 阅读关注点
- 应核对随机缺失假设、简单与一般模式的界定、优势比正确指定的要求，以及并入双重稳健程序后需满足的条件。
- 阅读边界
- 仅据版本未注明的索引摘要；一般模式的一致性依赖优势比正确建模，不能将简单模式的稳健性或效率推广到全部模式。
原文摘要
Robustness of covariate modeling for the missing-covariate problem in parametric regression is studied under the missing-at-random assumption. For a simple missing-covariate pattern, nonparametric covariate model is proposed and is shown to yield a consistent and semiparametrically efficient estimator for the regression parameter. Total robustness is achieved in this situation. For more general missingcovariate patterns, a novel semiparametric modeling approach is proposed for the covariates. In this approach, the covariate distribution is first decomposed into the product of a series of conditional distributions according to the overall missing-data patterns, and the conditional distributions are then represented in the general odds ratio form. The general odds ratios are modeled parametrically, and the other components of the covariate distribution are modeled nonparametrically. Maximum semiparametric likelihood is used to find the parameter estimates. The proposed method yields a consistent estimator for the regression parameter when the odds ratios are modeled correctly. In general, the semiparametric covariate modeling strategy increases the robustness against covariate model misspecification when compared with the parametric modeling strategy proposed by Lipsitz and Ibrahim. The new covariate modeling approach can also be incorporated into the doubly robust procedure of Robins et al. to increase protection against misspecification of the missing-data mechanism. In addition, the proposed modeling strategy avoids the usually intractable integrations involved in the maximization of the incomplete-data likelihood with parametric covariate models. The proposed method can be applied to many regression models to handle incomplete covariates.