Extension of the stein estimating procedure through the use of estimating functions

Kung Yee Liang, Myron A. Waclawiw

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This article extends the Stein method through the use of estimating functions (Godambe 1960) to address the simultaneous estimation of k population parameters, θ1, …, θk, in a mixed model setting. The procedure generalizes the Stein method by (a) allowing us to deal effectively with complications, such as inequality of population variances, that may arise in non-Gaussian mixed models; (b) being appropriate for estimating θi in populations of varying sizes and, in particular, populations of small sizes; and (c) applying to situations where it cannot be assumed that the θi’s have unbiased estimators or even estimators of finite moment. The focus of the article is on the quadratic variance function exponential family (Morris 1983b). Estimators for the parameters of the mixed model are developed in a regression model setting in which the θi’s are allowed to vary with a vector of covariates. An application to incidence rates for the Iceland Breast Cancer Incidence Data is presented for illustrative purposes.

Original languageEnglish (US)
Pages (from-to)435-440
Number of pages6
JournalJournal of the American Statistical Association
Issue number410
StatePublished - Jun 1990
Externally publishedYes


  • Conjugate prior
  • Empirical Bayes estimator
  • Exponential family
  • Maximum likelihood estimator
  • Mixed model
  • Score equation
  • Stein estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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