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

Annals of the Institute of Statistical Mathematics volume 63, pages 497–509 (2011)Cite this article

Abstract

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.

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Affiliations

  1. Division of Epidemiology and Biostatistics, School of Public Health, University of Illinois at Chicago, 1603 West Taylor Street, Chicago, IL, 60612, USA

    Hua Yun Chen

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  1. Hua Yun Chen
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Correspondence to Hua Yun Chen.

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Chen, H.Y. Representations of efficient score for coarse data problems based on Neumann series expansion. Ann Inst Stat Math 63, 497–509 (2011). https://doi.org/10.1007/s10463-009-0231-7

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  • DOI: https://doi.org/10.1007/s10463-009-0231-7

Keywords

  • Auxiliary variable
  • Adjoint operator
  • Coarsening at random
  • Nonparametric information operator
  • Projection