Abstract

Item nonresponse is frequently encountered in practice. Ignoring missing data can lose efficiency and lead to misleading inference. Fractional imputation is a frequentist approach of imputation for handling missing data. However, the parametric fractional imputation may be subject to bias under model misspecification. In this article, we propose a novel semiparametric fractional imputation (SFI) method using Gaussian mixture models. The proposed method is computationally efficient and leads to robust estimation. The proposed method is further extended to incorporate the categorical auxiliary information. The asymptotic model consistency and $\sqrt{n}$-consistency of the SFI estimator are also established. Some simulation studies are presented to check the finite sample performance of the proposed method. Supplementary materials for this article are available online.

摘要

项目不响应在实践中经常遇到。忽略丢失的数据可能会降低效率并导致误导性推理。分数插补是用于处理缺失数据的常用插补方法。但是，在模型错误指定的情况下，参数分数插补可能会受到偏差。在本文中，我们提出了一种使用高斯混合模型的新型半参数分数插补 (SFI) 方法。所提出的方法在计算上是有效的并且导致稳健的估计。所提出的方法被进一步扩展以合并分类辅助信息。渐近模型一致性和$\sqrt{n}$- SFI 估计量的一致性也被建立。提出了一些模拟研究来检查所提出方法的有限样本性能。本文的补充材料可在线获取。