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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bickel P., Klassen C., Ritov Y., Wellner J. (1993) Efficient and adaptive estimation for semiparametric models. John Hopkins University Press, Baltimore
Chen, H. Y. (2009). Estimation and inference based on Neumann series approximation to locally efficient score in missing data problems. Scadinavian Journal of Statistics, in press.
Heitjan D.F. (1994) Ignorability in general incomplete data models. Biometrika 94: 701–708
Heijtan D.F., Rubin D.B. (1991) Ignorability and coarse data. Annals of Statistics 19: 2244–2253
Kantorovich L.V., Akilov G.P. (1982) Functional analysis (2nd ed.). Pergamon Press, Oxford
Little R.J.A., Rubin D.B. (2002) Statistical analysis with missing data (2nd ed.). Wiley, New York
Nan B., Emond M.J., Wellner J.A. (2004) Information bounds for Cox regression models with missing data. Annals of Statistics 32: 723–735
Robins J.M., Wang N. (1998) Discussion on the papers by Forster and Smith and Clayton et al. Journal of Royal Statistical Society, Ser. B 60: 91–93
Robins J.M., Rotnitzky A., Zhao L.P. (1994) Estimation of regression coefficients when some regressors are not always observed. The Journal of American Statistical Association 89: 846–866
Rotnitzky A., Robins J.M. (1997) Analysis of semiparametric models with nonignorable nonresponses. Statistics in Medicine 16: 81–102
Rubin D.B. (1976) Inference and missing data. Biometrika 63: 581–592
Scharfstein D.O., Rotnitzky A., Robins J.M. (1999) Adjusting for nonignorable drop-out using semiparametric nonresponse models (with discussion). The Journal of American Statistical Association 94: 1096–1120
Van der Laan M.J., Robins J.M. (2003) Unified methods for censored longitudinal data and causality. Springer, New York
Yu M., Nan B. (2006) Semiparametric regression models with missing data: the mathematical review and a new application. Statistica Sinica 16: 1193–1212
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10463-009-0231-7