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Biometrika 1990 77(4):905-908; doi:10.1093/biomet/77.4.905
© 1990 by Biometrika Trust
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Miscellanea

On coherence in parametric density estimation

J. AITCHISON

Statistics Division, Department of Mathematics, University of Virginia Charlottesville, Virginia 22903, U.S.A.

In parametric density estimation the existence of a prior distribution on the parameter dictates the use of the corresponding predictive density function as estimate. This paper argues that in a decision theory approach to parameter density estimation any loss function introduced should lead to this predictive result for situations where prior information is available. The KullbackLeibler directed divergence has this coherence property whereas the corresponding symmetric divergence does not. The role of a recently suggested sequential improvement criterion in density estimation is also discussed.

Key Words: Admissibility • Coherence • Kullback-Leibler divergence • Predictive density • Sequential improvement


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