Skip to main content

Some model-restricted shrinkage estimators for contingency tables with missing data

Abstract.

For contingency tables with extensive missing data, the unrestricted MLE under the saturated model, computed by the EM algorithm, is generally unsatisfactory. In this case, it may be better to fit a simpler model by imposing some restrictions on the parameter space. Perlman and Wu (1999) propose lattice conditional independence (LCI) models for contingency tables with arbitrary missing data patterns. When this LCI model fits well, the restricted MLE under the LCI model is more accurate than the unrestricted MLE under the saturated model, but not in general. Here we propose certain empirical Bayes (EB) estimators that adaptively combine the best features of the restricted and unrestricted MLEs. These EB estimators appear to be especially useful when the observed data is sparse, even in cases where the suitability of the LCI model is uncertain. We also study a restricted EM algorithm (called the ER algorithm) with similar desirable features.

This is a preview of subscription content, access via your institution.

Author information

Authors and Affiliations

Authors

Additional information

Received: July 1999

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wu, L., Reeves, J. & Perlman, M. Some model-restricted shrinkage estimators for contingency tables with missing data. Metrika 50, 221–245 (2000). https://doi.org/10.1007/s001840050047

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s001840050047

  • Key words: Sparse data
  • empirical Bayes estimator
  • lattice conditional independence model
  • EM algorithm
  • restricted maximum likelihood estimator