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Monotone empirical Bayes estimators for the continuous one‐parameter exponential family
Author(s) -
Houwelingen J.C. van,
Stijnen Th.
Publication year - 1983
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1983.tb00796.x
Subject(s) - monotone polygon , mathematics , isotonic regression , estimator , exponential family , bayes' theorem , computation , simple (philosophy) , exponential function , property (philosophy) , statistics , bayesian probability , algorithm , mathematical analysis , philosophy , geometry , epistemology
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.