Representations of efficient score for coarse data problems based on Neumann series expansion.

We derive new representations of the efficient score for coarse data problems based on Neumann series expansion. The representations can be applied to both ignorable and nonignorable coarse data. An approximation to the new representation 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 coarse data 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.