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Monotone empirical Bayes estimators for the continuous one‐parameter exponential family

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  • J.C. van Houwelingen
  • Th. Stijnen

Abstract

A class of empirical Bayes estimators (EBE's) is proposed for estimating the natural parameter of a one‐parameter exponential family. In contrast to related EBE's proposed and investigated until now, the EBE's presented in this paper possess the nice property of being monotone by construction. Based on an arbitrary reasonable estimator of the underlying marginal density, a simple algorithm is given to construct a monotone EBE. Two representations of these EBE's are given, one of which serves as a tool in establishing asymptotic results, while the other one, related with isotonic regression, proves useful in the actual computation.

Suggested Citation

  • J.C. van Houwelingen & Th. Stijnen, 1983. "Monotone empirical Bayes estimators for the continuous one‐parameter exponential family," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 37(1), pages 29-43, March.
    • Handle: RePEc:bla:stanee:v:37:y:1983:i:1:p:29-43
    DOI: 10.1111/j.1467-9574.1983.tb00796.x
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    Cited by:

    1. Zhang, Shunpu & Karunamuni, Rohana J., 1997. "Bayes and empirical Bayes estimation with errors in variables," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 23-34, April.

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