During the past few decades, missing-data problems have been studied extensively, with a focus on the ignorable missing case, where the missing probability depends only on observable quantities. By contrast, research into non-ignorable missing data problems is quite limited. The main difficulty in solving such problems is that the missing probability and the regression likelihood function are tangled together in the likelihood presentation, and the model parameters may not be identifiable even under strong parametric model assumptions. In this paper we discuss a semiparametric model for non-ignorable missing data and propose a maximum full semiparametric likelihood estimation method, which is an efficient combination of the parametric conditional likelihood and the marginal nonparametric biased sampling likelihood. The extra marginal likelihood contribution can not only produce efficiency gain but also identify the underlying model parameters without additional assumptions. We further show that the proposed estimators for the underlying parameters and the response mean are semiparametrically efficient. Extensive simulations and a real data analysis demonstrate the advantage of the proposed method over competing methods.

中文翻译：

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不可忽略的缺失数据的基于全半参数似然的推理

在过去的几十年中，缺失数据问题得到了广泛的研究，重点是可忽略的缺失情况，其中缺失概率仅取决于可观察量。相比之下，对不可忽略的缺失数据问题的研究非常有限。解决此类问题的主要困难在于，缺失概率和回归似然函数在似然表示中纠缠在一起，即使在强参数模型假设下，模型参数也可能无法识别。在本文中，我们讨论了不可忽略缺失数据的半参数模型，并提出了一种最大全半参数似然估计方法，它是参数条件似然和边际非参数有偏采样似然的有效组合。额外的边际似然贡献不仅可以产生效率增益，还可以在没有额外假设的情况下识别基础模型参数。我们进一步表明，为基础参数和响应均值提出的估计量是半参数有效的。广泛的模拟和真实的数据分析证明了所提出的方法优于竞争方法的优势。