We derive new representations of the efficient score for the coarse data problems based on Neumann series expansion. The representations can be applied to both ignorable and nonignorable coarse data. Approximations to the new representations may be used for computing locally efficient scores in such problems. We show that many of the successive approximation approaches to the computation of the locally efficient score proposed in the literature for such problems can be derived as special cases of the representations. In addition, the representations lead to new algorithms for computing the locally efficient scores for the coarse data problems.

中文翻译：

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基于诺依曼级数展开的粗数据问题的有效得分表示

我们基于诺依曼级数展开推导出粗数据问题的有效分数的新表示。这些表示可以应用于可忽略和不可忽略的粗数据。新表示的近似值可用于计算此类问题中的局部有效分数。我们表明，许多用于计算文献中针对此类问题提出的局部有效分数的逐次逼近方法可以作为表示的特殊情况导出。此外，这些表示导致用于计算粗数据问题的局部有效分数的新算法。